After normal time failed to bring a goal, Negredo got ahead of his marker to prod home Dzeko's cross at the near post.
Read below to see how the action unfolded at St James' Park.
6.47pmHello, and welcome to Sports Mole's coverage of the Capital One Cup match between Newcastle United and Manchester City.
6.49pmSo after last night's games brought a flurry of goals, two more of the last-16 ties are to be played tonight. Will we see the same kind of level of goalmouth action?
6.51pmThe team news is already in from St James' Park. Let's have a look at who has made the cut, shall we?
6.52pmNEWCASTLE UNITED XI: Krul; Debuchy, Williamson, Yanga-Mbiwa, Haidara; Sissoko, Tiote, Anita, Gouffran; Shola Ameobi, Cisse
6.54pmNEWCASTLE UNITED SUBSTITUTES: Elliot, Dummett, Cabaye, Sammy Ameobi, Ben Arfa, Obertan, Remy
6.59pmNewcastle boss Alan Pardew has made several changes to the team that lost to Sunderland at the Stadium of Light on Sunday afternoon. Mapou Yanga-Mbwia has been recalled in defence after sitting out the last match through suspension, while Shola Ameobi has been given a start up front.
7.00pmThe three star men for the Magpies - Yohan Cabaye, Hatem Ben Arfa and Loic Remy - are all amongst the substitutes.
7.02pmAs for Manchester City, there is a notable absentee...
7.04pmMANCHESTER CITY XI: Pantilimon; Richards, Boyata, Lescott, Kolarov; Rodwell, Garcia; Navas, Jovetic, Milner; Dzeko
7.05pmMANCHESTER CITY SUBSTITUTES: Hart, Zabaleta, Nasri, Negredo, Silva, Fernandinho, Demichelis
7.07pmManchester City manager Manuel Pellegrini has retained just one of the starting lineup that began against Chelsea at the weekend. Javi Garcia has kept his place in midfield, with three of the players - Matija Nastasic, Yaya Toure and Sergio Aguero - not included on the bench.
7.10pmYou will also notice that Joe Hart has been dropped by Pellegrini. I'm sure that the Chilean will insist that the England number one wouldn't have played this match anyway, but it does pose the question whether Hart has been dropped for his mistake at the weekend. I guess we will find out at the weekend...
7.14pmPellegrini has named an interesting team though. Plenty of the XI will be eager to impress their boss after their questionable showings on the road this season. Stevan Jovetic has hardly featured, Edin Dzeko has found himself out in the cold in recent weeks after the form of Aguero and Negredo, and Joleon Lescott has failed to get in the side, despite the injury to Vincent Kompany.
7.18pmThis isn't the first time that these two teams have met this season. Newcastle travelled to the Etihad Stadium on the opening weekend of the season, but after being disrupted by talk of Yohan Cabaye wanting away from the club, they slumped to a 4-0 defeat. Surely it can only get better this evening?
7.21pmMagpies boss Pardew said earlier this week that winning the Capital One Cup was one of his leading priorities this season. Given that he has named the likes of Cabaye, Ben Arfa and Remy on the bench, I'm sure there will be a few Newcastle fans questioning that comment, but I suppose Pardew will argue that he needs to give a few other players in the squad an opportunity to shine.
7.26pmAs usual, this isn't the only match that we are covering on Sports Mole this evening. There is the game at White Hart Lane between Tottenham Hotspur and Hull City to feast your eyes on, while there are also a couple of matches in Spain taking place tonight.
7.31pmPREDICTION! After their respective defeats at the weekend, you would expect a fast start from both sides. But Manchester City have the greater strength-in-depth of the two sides, and even if Newcastle hold the advantage after the hour-mark, you would expect City to hit back in the closing stages. A narrow City win, maybe during extra-time.
7.35pmWe are just 10 minutes away from kickoff at St James' Park. This may just be a Capital One Cup fixture, but expect to see a full house inside St James' Park tonight.
7.40pmI should have mentioned this earlier. Cheik Tiote is a lucky boy to be starting tonight - he narrowly avoided a prison sentence earlier this week for possessing a fake driving licence!
7.43pmThe two teams have walked out onto the pitch on Tyneside. A reminder that if we are level at normal time, we will play an extra 30 minutes.
0 minNewcastle get us underway.
3 minIt's a composed start from the visitors, but after working the ball forward, Dzeko gives the ball away when attempting to play in Milner down the right. Newcastle keep the ball until a long pass out of defence nearly reaches Ameobi.
6 minMuch of Manchester City's play is going through the middle with Rodwell and Garcia looking to get on the ball. They manage to get the ball to Jovetic in attack, but he is cynically brought down by Williamson, who is lucky to avoid a yellow card.
8 minNewcastle win a free kick on the left-hand side, but Anita's floated delivery is lacking in pace and is cleared.
9 minCHANCE! That was close! A long ball is flicked on by Ameobi into the path of Cisse, who lobs the ball marginally past the far post. His goal drought continues!
11 minSUBSTITUTION! That must be gutting for Jovetic. He has been forced to go off with what looks like a calf injury. He has been replaced by Alvaro Negredo.
15 minThe action has settled down a little now. Newcastle are largely in the ascendancy, but City are being patient in their approach once they retrieve the ball.
17 minCity finally make inroads into the Newcastle half, with Rodwell hitting the ground a bit too easily after pressure from Williamson. The ball landed at the feet of Milner, but his first-time effort was well blocked.
19 minGouffran looks to be struggling with a problem now, He dangled his foot out attempting to tackle Negredo, but he looks to have come off worse.
23 minIn tonight's other Capital One Cup tie, Spurs have taken the lead against Hull City, thanks to a goal from Sigurdsson. It looks as though it is going to be a pretty strong last-eight lineup.
24 minThe quality in the final third has been poor so far, and that trend continues when Milner crosses straight into the stand with Dzeko waiting in the middle.
27 minOUCH! That looked a weird incident. Milner rises to challenge for a high ball with Yanga-Mbwia, but after hitting the deck, he immediately holds his knee. The England international is back on his feet, but he looked in trouble for a minute there.
30 minCHANCE! That's better from Newcastle. After Sissoko sees an effort blocked by Lescott, Ameobi sent a volley from 12 yards arrowing towards the bottom corner, but he is well denied by Pantilimon.
32 minDISALLOWED GOAL! Milner handles the ball in the right-hand corner of the pitch to gift Newcastle a set piece. Anita's cross finds Cisse, who scuffs a tremendous opportunity, but the ball went straight to Ameobi, who netted at the back post. However, the assistant rightly put up his flag with Ameobi marginally offside.
34 minCHANCE! Newcastle are battering City! A cross to the back post is only half cleared by Boyata to Anita, who sends a first-time volley flying just past the post. Newcastle need to capitalise while they have the visitors on the back foot.
37 minBOOKING! The first booking of the match is handed to Garcia, who mis-time a challenge on Haidara on the left. The full-back is still down receiving treatment, but he will be fit to carry on.
40 minThere are five minutes remaining before the break, Newcastle won't want this half to end. City haven't come close to playing well during this opening 45 minutes, and Pellegrini will be eager to get his team back into the dressing room.
45 minMicah Richards goes on an incredible run from his own half, but the end product isn't there - in fact, that is an abysmal effort! There will be two minutes of added-on time.
45 minNewcastle win a late corner, which Pantilimon flaps at, but City clear. That's the first moment of uncertainty from the goalkeeper.
45+2 minBOOKING! Tiote is the first Newcastle man to receive a booking this evening after flying through the back of Garcia, who is left on a heap on the ground.
45+2 minHALF TIME: Newcastle United 0-0 Manchester City
8.37pmThat brings an end to the opening 45 minutes at St James' Park, and we remain goalless. It took a while for the action to intensify, but when it did, it was Newcastle who looked the more likely to net an opener, but City did well to survive. Alan Pardew will be hoping that they aren't made to pay for their failings in front of goal.
8.41pmNewcastle's supremacy is highlighted in the half-time stats. They have had six shots to Man City's three, with the visitors failing to have a shot on target. It probably won't be too long before Pellegrini changes things for a second time in attack.
8.45pmAt White Hart Lane, it remains 1-0 to Spurs. Given their impressive clean sheet record this season, that match could be done and dusted.
46 minNewcastle have made a change at half time, bringing on Dummett for Haidara, who couldn't have recovered from the problem he picked up shortly before the interval. We have restarted at St James' Park.
50 minSHOT! Newcastle have started like they finished. Some crisp passing from the back engineered some space for Anita to stride forward, but his long-range shot was well claimed by Pantilimon.
53 minMore pressure from Newcastle earns them their third corner of the match. However, Anita is maintaining his flighted-delivery approach, and it goes straight into the grateful hands of Pantilimon.
55 minCHANCE! It's Manchester City's turn to try to break the deadlock. A corner from the right ends up on the far side, but Milner swings the ball back in for Richards to head just over.
59 minCity win another corner, and like the one a few minutes ago, no-one can connect. However, the danger isn't over, and after a Milner effort is blocked, Rodwell slices a volley over, which was a tad ambitious to say the least.
60 minMaybe I spoke too soon about Spurs advancing to the quarter-finals? Hull have equalised through an own goal from Brad Friedel.
63 minCHANCE! Tim Krul, you lucky boy. The Newcastle stopper gets into a muddle on the edge of his area, and he is dispossessed by Navas. The Spaniard then played the ball to Milner, who sent a powerful effort from around 35 yards over the crossbar with Krul still attempting to get back between his posts.
66 minSUBSTITUTIONS! Both sides make an alteration. For Newcastle, Yohan Cabaye enters the fray in place of Ameobi, while the visitors bring on David Silva for Rodwell.
70 minCabaye attemptd to make an instant impact after his introduction, but his 30-yard shot was never troubling Pantilimon. There's just 20 minutes remaining of normal time. Are we heading for extra-time?
72 minTiote looks in severe discomfort after a collision with Micah Richards. The City defender looked to have come off the worse of the two, but it's the Newcastle player who is still down receiving treatment.
75 minYanga-Mbiwa is limping as well for Newcastle, but both he and Tiote are going to continue for now. Navas nearly exploits the home side's struggles with a break down the right, but his cross is headed wide by Dzeko.
77 minNeither side are playing for extra-time, but no-one is going to break the deadlock until the final ball improves.
78 minCHANCE! How has Negredo missed that? Dzeko plays in the Spaniard, who feints to shoot about half a dozen times before attempting to clip the ball over Krul. However, the Dutch goalkeeper is equal to the task and tips the ball wide.
82 minBoos ring around St James' Park, and I'm not surprised. Micah Richards goes down with a touch of cramp with Newcastle on the attack, and Tiote opts to play the ball out for a throw-in. That was rather generous. Ben Arfa is on for the home side.
85 minI'm afraid that there has been nothing forthcoming in terms of shots on goal. It's looking like extra-time...
88 minCHANCE! Manchester City apply a little bit of pressure down the left through Negredo and Kolarov. The leftback crosses to the back post from Dzeko, whose header is well tipped away by Krul.
90 minThere will be four minutes of added-on time.
90+2 minBOOKING! David Silva gets a yellow card for kicking the ball away after City concede a free kick. One last chance for Newcastle.
90+4 minFULL TIME: Newcastle United 0-0 Manchester City
9.39pmThe 90 minutes are up at St James' Park, and we are heading into extra-time. Things will have to improve or else it is a certainty that we will have penalties.
91 minManchester City get us back underway.
91 minIt's worth noting that both teams have already made all three changes.
93 minCHANCE! Will Papiss Cisse ever score a goal again? He will never get a better chance than that. The ball was played beautifully over the top for the forward to bring down in space, but with just Krul to beat, he struck the ball straight at the goalkeeper.
98 minManchester City are attempting to force the issue, but at the moment, it is coming to no avail. Dzeko had an opportunity to head towards goal from six yards, but he jumped too early and he glanced wide.
99 minGOAL! Newcastle United 0-1 Manchester City (Negredo)
99 minWE HAVE A GOAL! After 99 minutes of the more uninspiring action you will see this season, Manchester City are ahead. Dzeko did fantastically down the left before driving a low cross into the box, where Negredo got ahead of Yanga-Mbiwa to prod home.
103 minHave Newcastle got the energy to reply to that opener? You get the feeling that it is going to take something special from the likes of Cabaye or Ben Arfa if the Magpies are going to rescue this game.
105 minGOAL! Newcastle United 0-2 Manchester City (Dzeko)
105 minThere's going to be no coming back from that. Manchester City score a terrific second through Dzeko, who latched onto a pass from Milner before taking the ball around Krul and tapping the ball into an empty net.
105+1 minHALF TIME: Newcastle United 0-2 Manchester City
107 minThat second goal saw many of the home crowd make for the exit, and I can't really blame them. There is still 10 minutes remaining, but the damage has been done.
109 minSHOT! Milner very nearly makes it three for City, but he drags his 20-yard effort just wide, via the fingertips of Krul.
113 minOFF THE LINE! So close for the Magpies. Cabaye is slowly becoming more instrumental in the middle of the park, and he nearly reduces the deficit. His shot was heading for the bottom corner, only for Lescott to divert the ball behind for a corner.
116 minSHOT! The visitors are almost showboating in the final third of the pitch, before setting up an opportunity for Silva. He dinked inside the defender on the edge of the area before curling the ball fractionally wide.
120 minFULL TIME: Newcastle United 0-2 Manchester City
10.17pmThe referee brings an end to what has been a long night at St James' Park. Manchester City have progressed through to the quarter-finals of the Capital One Cup after finally getting the better of Newcastle United after an extra 30 minutes.
10.18pmIt was tough on the home side, after they had performed the better during normal time. However, there was only one team in it during the extra period, and City remain a force in the competition.
10.20pmThat will be all from Sports Mole for this match. Thank you for joining us, despite the action not being edge-of-your-seat stuff! Goodbye for now.