Ghana struck the post early in the added 30 minutes but it was Chile who regained the lead through Henriquez's second of the match.
Seidu Salifu levelled the sides again in the 112th minute before Assifuah headed his side into the semi-finals in the last minute of extra time.
You can read how an enthralling 90 minutes unfolded with Sports Mole's play by play coverage below.
6.58pmGood evening! Thank you for joining Sports Mole a little later than scheduled due to the dramatic first quarter-final of the day. Iraq have just booked their place in the last four courtesy of a 5-4 win on penalties against Korea.
6.59pmTime to turn out attention to this match, however, and we're almost ready to go here. Ghana began this tournament in shaky form but have begun to fulfil some of their potential in their last couple of matches.
0 minKICKOFF: Here we go! Ghana get us underway in this one. Who will reach the last four to face France on Wednesday?
1 minFast start to this match as Chile look to put Ghana under heavy pressure when the Africans are in possession. Ghana win an early corner but it comes to nothing.
3 minCHANCE! Good chance early on for Chile as Bravo makes his way down the right flank before sending a cross over to the unmarked Baeza. The ball is slightly behind him so he goes for an acrobatic scissor kick, but shins it well over the bar. He had more time than he thought there.
5 minGhana are a side who tend to finish strongly. In this competition so far, five of their eight goals have come in the last 15 minutes.
6 minThat is very ambitious from Robles. The centre-back must be all of 40 yards out and he goes for goal. Predictably, he drags it harmlessly wide.
7 minCHANCE! Good play from Ghana there as Boakye takes the ball in his stride inside the box before attempted a curling effort into the far corner. He just can't wrap his foot around it, however, and it ends up a couple of yards wide.
9 minIt's has been a good, high-tempo start to this match. Both sides look eager to get forward in numbers and, if it carries on like this, we could be treated to a few goals in this one.
10 minYiadom Boakye in particular looks in the mood this evening. The striker plays his club football for Juventus and is really one to watch for Chile.
12 minOh what a fine goal that is! Chile are struggling to deal with Ghana's pace and power early on, and that was clear to see there. Acheampong played a one-two with Baba before dinking a cross to an unmarked Odjer at the back post. The midfielder brought it down on his chest before firing a well-controlled but powerful volley into the top corner. Brilliant goal.
13 minThis match has been played at a frenetic pace so far. If it carries on like this, then we are in for a highly entertaining contest!
15 minCastillo almost connects with a vicious ball into the box. Ghana need to keep a very close eye on Castillo today, he is Chile's most dangerous player by some distance.
17 minAssifuah goes down in a heap after a high foot from Robles caught him flush in the face. Ghana have a free kick in a good crossing position, but they will be concerned that Assifuah is now being stretchered off.
19 minThese Chilean defenders seem confident in their ability to hit the ball from range, and so far that confidence seems to be misplaced. This time it is Larenas who lines up an effort from 40 yards, but he puts it a long way wide.
21 minChile now have a free kick in a dangerous crossing position after a clumsy challenge from Odjer...
22 min...but nothing comes of it as it is cleared by the first man.
24 minWow! That is why he is their dangerman. An absolutely stunning strike from Castillo levels the sides in style. Bravo robs a Ghana player of possession before poking the ball through to the striker, who still has plenty to do. He is over to the right of the area and has very little of the goal to aim for, but he puts everything into the shot and hammers it past the keeper. Magnificent goal.
26 minThose are two goals of the highest quality we have seen in this match already, and I wouldn't bet against seeing more. The Iraq vs. Korea game that we have just seen could claim to be the match of the tournament so far but, the way this one is shaping up, it could challenge it!
28 minIt's a quickfire double from Chile! This match really is shaping up nicely. The ball is fed into the feet of Manchester United's Angelo Henriquez and he turns away from Nketiah before firing a low shot into the corner on the turn from the edge of the area. It's another fine goal, albeit not as clean a strike as the other two. Advantage Chile!
29 minSHOT! Aboagye tries to find an immediate response for Ghana with a shot from 25 yards out, but he drags his effort harmlessly wide.
31 minGhana have responded well to that double blow. They almost find shooting space inside the area through Acheampong, but he never really has full control of the ball and is eventually crowded out by the defence.
33 minThere is a great energy all over the field for both sides. Neither set of players are pulling out of 50/50 challenges and there is an obvious hunger and desire to win this one.
35 minCLOSE! Castillo really does have a good strike on him. Chile break again and the ball falls to Baeza on the edge of the box. He turns down the chance to shoot himself, instead setting up Castillo, who fizzes a first-time curling effort just over the bar.
37 minChile have edged the possession stats so far, although they have probably only moved clear in the last 10 minutes or so. They have seen 54% of the ball compared to Ghana's 46%.
38 minCampos gives the ball away to Acheampong, who immediately races into the area before trying to drill a low cross towards Assifuah who is unmarked in the area. It is well defended by Lichnovsky, however, who puts it behind for a corner.
39 minAcheampong causes Campos trouble again as he gets the wrong side of the Chilean full-back. Once again, though Lichnovsky comes across to thwart the lively Ghanaian.
41 minCLOSE! Chile come close to extending their lead further. A dangerous free kick is whipped in to the near post where Robles meets it, but his header ends up the wrong side of the post as far as he is concerned, thumping against the side netting.
42 minBaba skips in between two tackles with apparent ease, but his final ball doesn't match the approach play as it is cut out and cleared by Robles.
43 minYELLOW CARD! Lartey becomes the first man in the referee's book, which means that the Ghana skipper would miss the semi-final if they make it there. The caution was for a late tackle from behind on Castillo, who made the most of it.
45 minThere will be one minute of added time at the end of this half.
7.49pmThe referee brings an end to fine half of football which has seen Chile overturn a 1-0 deficit to lead 2-1 at the break. We have been treated to some special goals along the way, too.
7.51pmGhana opened the scoring through Moses Odjer, who controlled a cross before smashing a sweetly-struck volley into the top corner, but Chile were soon level when Nicolas Castillo produced his own moment of magic, hammering the ball in at the near post from a tight angle. Then, moments later, Angelo Henriquez lost his man on the edge of the area before turning and shooting into the bottom corner.
7.53pmIt has been an entertaining, open game so far with plenty of sights of goal for both sides. The emphasis is very much on attack, which is great news for any neutrals!
7.55pmAs expected, Nicolas Castillo has been very impressive for Chile. He took his goal brilliantly and has shown flashes of what else he can do on a couple of occasions. For Ghana, Yiadom Boakye started well but it is Frank Acheampong of Anderlecht who has caused the biggest problems.
7.57pmThis is the last quarter-final of these Under-20 World Cups, and it is worth reminding you that the winners will go on to face France in the semis on Wednesday.
7.59pmThe other semi-final has already been decided as Uruguay, who beat tournament favourites Spain yesterday, will take on Iraq, who beat Korea on penalties after a dramatic 3-3 draw just before this match.
8.01pmAs things stand, Ghana are on their way out of the competition, which would be disappointing for a side who won it in 2009. Having said that, they also failed to qualify for the last edition two years ago, so a quarter-final appearance is a decent showing for them.
8.02pmThey have also been runners-up twice, so they have plenty of history in this competition.
8.03pmRight, the teams are back out on the pitch ahead of this second half. Can Ghana come back or will Chile hold out for a place in the final four?
45 minKICKOFF: Chile get us back underway in Istanbul.
46 minGood start to the second half as Acheampong finds space behind the defence yet again. He drills a low cross into a very dangerous area and all it needs is a touch for a certain goal, but it is just behind Boakye which allows Chile to clear.
47 minBoakye bundles his way through a couple of challenges before pushing the ball past Baeza. He realises that he won't get to it the other side so throws himself to the floor right in front of the ref, who rightly tells him to get up. He's lucky not to be booked there.
48 minSAVE! Ghana have made a very strong start to this half. The ball is played back to Salifu who lets fly from 25 yards out, but his well-struck effort is straight at the keeper, who holds on to it.
50 minChile are struggling to deal with Ghana at the moment. They break away again but Chile have just enough bodies back to get a block in before clearing the danger.
52 minSAVE! Out of nothing, Chile almost grab a third goal, and it is Castillo who nearly sneaks it in at the near post again. It would have been a carbon copy of his first goal, but this time Antwi is alert to the danger and pushes it away.
53 minSAVE! Antwi is called upon again to keep his side in it there! Henriquez gets away from his marker before firing a powerful strike that looks destined for the top corner until the Ghana keeper flies across his goal to tip it wide at full stretch. Good save.
54 minAntwi is in action again as he gets a strong hand to a low cross, but he only pushes it out to a number of Chile players lying in wait. The defence gets out to them quickly and the eventual shot strikers Henriquez.
55 minBoakye shows good strength to hold off his man as he spins round him, only to drag his shot tamely wide. Chance after chance for both sides at the moment.
57 minSAVE! That is a top save from Melo! A long ball into the box finds Acheampong at the back post and he chests it down before smashing a powerful effort goalwards from point blank range. Melo is out bravely to smother the shot, however, tipping it wide for a corner.
58 minCLOSE! Ghana are putting the pressure on now, and it is Salifu who comes close this time. He gets the ball 25 yards out and takes a touch before hammering his strike just wide. Melo was rooted to the spot there, he wouldn't have reached it if it was on target.
60 minNketiah is down injured which leaves Ghana short of defenders at the back. Chile don't kick the ball out, but they can't make the most of a four on three situation, coming out with only a corner.
62 minGHANA SUB: Ghana have been short at the back since Nketiah was forced off with that injury, and finally they will replace him. On comes Princebell Addico.
63 minYELLOW CARD: Chile have a free kick in a good position, but Rabello is taking too long to take it for the referee's liking and is shown a yellow card for time wasting. Very harsh decision.
65 minSAVE! Boakye cuts inside from the left flank on to his right foot before hitting a low shot towards the near post. Melo is equal to the effort, however.
67 minSAVE! These two sides seem to have a pact to only score wondergoals in this match! Rabello goes for goal from between 35-40 yards out and strikes it well enough, but it is straight at Antwi, who holds on to it.
68 minCHANCE! Baba tries to keep up the wondergoals-only rule by controlling the ball on his knee and volleying it. Lichnovsky blocks the initial shot, but the ball falls kindly for Baba again, only for him to snatch at the chance and slice it high and wide.
69 minGHANA SUB: Boakye is making way for Ghana, and he doesn't look too happy about it. He trudges off to be replaced by Kennedy Ashia.
70 minSAVE! Assifuah shows good strength to hold off his man before getting a shot away that Melo has to tip wide for a corner.
71 minCHILE SUB: Larenas is forced off on a stretcher to be replaced by Cristian Cuevas.
73 minGhana are back level! It is good play by Aboagye on the edge of the box as he keeps the ball despite three Chile defenders nipping at his heels. He looks to have done too much before feeding the ball to Assifuah with the outside of his foot, and the Ghana striker takes a touch before poking the ball past Melo. Not quite as good as the other goals we have seen today, but no less important.
75 minAssifuah is becoming more and more involved in this one now. He lines up a defender on the right before showing great acceleration to beat him and get to the byline, but he can't wrap his foot around the ball to get a cross in.
77 minCHANCE! Oh Ghana could and probably should be ahead here! The Chilean defence is non-existent as Assifuah is released through on goal. The keeper is forced to come out and he does just enough. He gets a touch to the ball, which rebounds back off Assifuah but knocks him off balance, and he falls over as Robles clears it from in front of the open goal. Had Assifuah managed to stay on his feet there it would have been 3-2.
79 minCHILE SUB: Lichnovsky makes way for Chile to be replaced by Valber Huerta.
80 minCHANCE! Pass it! Pass it! Pass it! Rabello twists and turns on a counter attack with three Ghana defenders and the keeper surrounding him. He has Bravo screaming for the ball completely unmarked but chooses not to play the simple square ball and is eventually crowded out. Poor decision making.
81 minCHANCE! Acheampong is a real handful. He somehow gets away from two defenders inside the box again before seeing his powerful strike from close range very well blocked. This is end to end stuff at the moment!
83 minCLOSE! Ghana come close again, this time through Baba. He hits his long range shot first time and, although he doesn't catch it very sweetly, it rolls very narrowly wide.
84 minCHILE SUB: Chile's third and final sub sees Campos replaced by Nicolas Maturana, which is a bit of an attacking sub. A midfielder brought on for a defender.
86 minCastillo almost finds a late opening as Ghana fail to deal with a low cross into the box, but the Chile striker's effort is deflected behind for a corner.
87 minThere seems to be so much space for both sides at the moment, which makes for great viewing. I wouldn't be surprised to see a late winner, but I want another 30 minutes!
88 minYELLOW CARD! 16-year-old Moses Odjer will miss the semi-final if Ghana make it now. He picks up his second yellow of the tournament for a foul on Cuevas.
90 minThere will be four minutes of added time for either side to find a dramatic late winner.
90+2 minIt is Chile who look most likely to get a winner at the moment. They are seeing a lot more of the ball and are pinning Ghana back, but the African side can be deadly on the counter-attack.
90+3 minFrom one such counter Baba wins a corner for his side. Perhaps one last chance to get a winner?
90+3 minThat would have been some way to win it! The corner isn't the best and is headed straight up in the air. Assifuah is waiting underneath and pulls off an ambitious bicycle kick that ends up high over the bar.
8.54pmSo, for the second time today we will go to extra time in an Under-20 World Cup quarter-final. Tiredness will now begin to play a part, especially considering how much they have put into this game already. It is worth noting that Chile have used all three subs, while Ghana have one left.
8.56pmWhile it may be a trial for the players, an extra 30 minutes of this match is a treat for the spectators. This has been a very good game of football so far, with plenty of chances and a couple of spectacular goals as well.
8.58pmThe goals have come from Moses Odjer, Nicolas Castillo, Angelo Henriquez and Ebenezer Assifuah. Can anyone else add their name to that list in the upcoming 30 minutes?
8.58pmBoth sets of players are embraced in their final huddle before this one gets back underway. It is as much about mental strength and physical fitness as it is about footballing ability now.
90 min ETKICKOFF: The referee blows the whistle to restart this match again, and Chile get us underway.
91 min ETOFF THE POST! What a start that would have been for Ghana, and it would have been another great goal! Acheampong receives the ball on the left side of the area and thumps a powerful effort towards the far top corner, only to see it tipped on to the inside of the post. Great save, great effort.
93 min ETCHANCE! What a start to extra time this is! Castillo is released completely through on goal and he only has the keeper to beat. Antwi stands up and makes himself big, but Castillo does him a huge favour by hitting it straight at him. He really should have scored there and, if you would've backed one player on this pitch to bury such a chance, it would be Castillo.
94 min ETSHOT! Yet another long range effort for Ghana - that's their 28th effort on goal today. It is Ashia who lets fly this time, and his strike whistles a yard or so past the post. Shots galore here.
95 min ETYELLOW CARD! Robles can have no complaints about that one. Attamah comes out of defences and embarks on a great run that takes him past three players. Just as he gets past the last man he is brought down by Robles, who picks up a yellow that would rule him out of the semi-final should Chile get there.
96 min ETFrom the resulting free kick the ball is given to Ashia who goes for another long range effort, but he whacks it into the wall.
97 min ETYELLOW CARD! Attamah becomes the latest player to pick up a yellow that would see him ruled out of the semis. He brings down Rabello and is rightly booked.
99 min ETWe've seen plenty of thunderous efforts in this one so far, but this one is beautifully delicate. Baeza clips a lovely ball over the top and no-one follows the run of Henriquez, who just flicks a cute little header over Antwi.
100 min ETSHOT! Aboagye looks to provide an instant response for his side with a powerful run through midfield, but his eventual shot is a yard over the bar.
101 min ETAmazingly, Ghana have hit the 30 shot mark in this match. That is twice as many as Chile's 15 efforts, and that isn't exactly a small tally! The only thing that matters is how many you score, though, and Ghana need at least one more here.
103 min ETSAVE! Assifuah shows good feet to get away from Huerta and create space for yet another shot, but his powerful effort is straight at Melo. It stings the Chilean keeper's palms, but he is able to collect at the second attempt.
105 min ETHALF TIME IN EXTRA TIME: Ghana 2-3 Chile
9.15pmThere is the end of the first half of extra time, and it has been another pulsating 15 minutes of football. Chile have the advantage ahead of the final moments, but Ghana have come back once already and will be confident of doing so again.
9.16pmGHANA SUB: One last throw of the dice for Ghana as they introduce the fresh legs of striker Francis Narh. He comes on for Moses Odjer, who scored the opening goal what feels like an eternity ago.
105 min ETKICKOFF: Ghana get us back underway for the final time here in Istanbul. Can the African side come back again to save their World Cup status?
107 min ETChile are packing the edge of the area which is forcing Ghana into long range shots. The latest comes from Ashia, who just tries a toe-poked snapshot towards the top corner, but Melo easily plucks it out of the air.
108 min ETCHANCE! Aboagye picks the ball up from Acheampong's pass before dancing past one tackle to create space to shoot from just inside the box. His effort lacks power, however, and is comfortable for Melo.
110 min ETYELLOW CARD! Assifuah picks up a yellow for an unnecessarily late challenge on the keeper as the ball ran through to him. A little frustration creeping into his game there, perhaps.
113 min ETThere is another twist in the tale! Ghana have equalised again, picking their way through a crowded and stubborn Chile defence. Aboagye played a one-two on the edge of the box before poking the ball into the path of Salifu, who was bursting into the box. The midfielder took a touch before calmly slotting it past the keeper to bring Ghana back into the match!
115 min ETCHANCE! Oh Ghana should probably be ahead now! Aboagye is becoming the conductor here as again he plays a fine through ball to Assifuah, who only has the keeper to beat. Melo comes out to close the angle well and Assifuah shoots with his right foot when he perhaps would have been better going with his left. He can only put it narrowly wide.
116 min ETYELLOW CARD! Henriquez becomes the latest player to enter the book for a cynical foul of Baba.
117 min ETCHANCE! Another great chance for Ghana goes begging! Acheampong floats a lovely ball into the box and Ghana players are queueing up to head it. It is Attamah who gets to the ball, but he can't get enough on it and glances it wide when he should have scored.
118 min ETSHOT! These shots are just relentless! This time it is Aboagye who goes for goal from 25 yards out, but he sends it wide of the post. It is all Ghana at the moment.
119 min ETAcheampong, who has been quite brilliant today, goes for goal this time and it deflects behind for a corner.
119 min ETThat is swiftly followed by shot number 39 for Ghana as Assifuah digs out an effort that ends up on the roof of the net via a deflection.
120 min ETGOAL! Ghana 4-3 Chile (Ebenezer Assifuah)
120 min ETOh my word! What drama here, and what an end to a magnificent football match. Acheampong is again instrumental as he makes his way to the byline before lifting a cross to Assifuah at the back post. His header looks soft, but two Chile defenders get in the way of the keeper and somehow it sneaks through into the net. It is a painfully soft goal to concede, especially at such a critical time in the game. Ghana are surely in the semi-finals now!
9.37pmWhat a simply superb game of football that was. A great advert for Under-20 football, but at any level that would have been a classic match. Istanbul has seen its fair share of dramatic matches in the past, namely the 2005 Champions League final, but this is almost up there with that. Superb match, one of the best I have seen for a long, long time. The Chile players are in tears, it must be heartbreaking to be eliminated like that.
9.39pmFrank Acheampong and Clifford Aboagye were instrumental for Ghana during that match. They performed brilliantly throughout and, without them, I doubt Ghana would have even made it to extra time. They now go on to face France in the semi-final on Wednesday, and if that is half the match we have seen today then we are in for a treat!
9.41pmChile will understandably be devastated right now, but they can hold their heads up high. They put in a very good performance this evening and neither side deserved to lose this one. Unfortunately someone has to, but they can leave in the knowledge that they have played their part in the game of the tournament so far.
9.43pmSo, our two semi-finals are now confirmed. First up on Wednesday will be France vs. Ghana to determine the first finalist of the 2013 Under-20 World Cup, before Iraq take on Uruguay in the second semi-final. The final, incidentally, is due to take place on Saturday.
9.43pmGhana had a quite frankly ridiculous 41 shots in that match, 22 of which were on target. Chile had 17 shots of their own as well, no wonder it was such an entertaining match!
9.45pmRight, that's it from me tonight. Thank you for joining Sports Mole for what was an enthralling game of football. Ghana eventually came out on top in the most dramatic fashion, scoring in the last minute of extra time to seal a 4-3 win. I hope you've enjoyed it as much as I have, and I will leave you with Michael Penkman's match report, and be sure to join us for the semi-finals on Wednesday. Until then, though, it's goodbye from me!