Second-half goals from James Rodriguez and Juan Quintera put the South American side ahead.
However, Gervinho got the Ivorians back into contention with a solo effort with 15 minutes still to play.
Read how all the action unfolded below:
4.02pmGood afternoon! It's just under a hour until Colombia and Ivory Coast will head out to the pitch in Brasilia for their second match of the World Cup. The teams have already been announced, so let's take a look at the lineups...
4.03pmCOLOMBIA STARTING XI: Ospina, Zuniga, Armero, Sanchez, Zapata, Yepes, Cuadrado, Aguilar, Gutierrez, Rodriguez, Ibarbo
4.05pmIVORY COAST STARTING XI: Barry, Aurier, Boka, Gonzaroua Die, Zokara, Bamba, Gradel, Tiote, Bony, Yaya Toure, Gervinho
4.06pmCOLOMBIA SUBSTITUTES: Arias, Carbonero, Vargas, Guarin, Mejia, Balanta, Ramos, Quintero, Martinez, Mondragon, Valdes
4.07pmIVORY COAST SUBSTITUTES: Diarrassouba, Kolo Toure, Bolly, Akpa-Akpro, Kalou, Drogba, Ya Konan, Diomande, Gbohouo, Djakpa, Sio, Mande
4.10pmSo the big news for the Ivory Coast is that Wilfried Bony is preferred up front to Didier Drogba. The Swansea City striker scored the first of the African side's two goals in their win over Japan on Saturday. Bony only out-and-out striker in the starting XI, but Yaya Toure and Gervinho should provide plenty of threat in front of goal for the Ivorians too.
4.13pmHaving cruised past Greece in their opening game, Colombia stick with the same starting lineup for this match. The only change for the South Americans is that they are without Carlos Bacca after he picked up a leg injury in the opening match, ruling him out of the rest of the tournament.
4.16pmThis will actually be the first time that these two nations have faced each other. Colombia coach Jose Pekerman has come up against the Ivory Coast in his previous role with Argentina though, coming away with a 2-1 win at the 2006 World Cup.
4.19pmThis is a big match for Colombia captain Mario Yepes, he picks up his 100th international cap for the country today. The defender made his debut in 1999, and has scored six goals in his previous 99 appearances.
4.22pmThis match will be English referee Howard Webb's first outing in this tournament. The 42-year-old impressed in the early stages of the 2010 event enough to be awarded the final, although came in for criticism for not controlling the highly-charged meeting Spain and the Netherlands.
4.25pmLet's take a closer look at the two sides' form heading into this match. Colombia looked impressive in their opening game, claiming their biggest ever win at the World Cup. They've never gone unbeaten in back-to-back matches at the World Cup before, but are unbeaten in their last eight outings.
4.28pmIvory Coast have been in mixed form recently, with two defeats, three wins and three draws in their last eight internationals. The Elephants have been shaky at the back over the last year, having not kept a clean sheet since their 3-0 win over Gambia last June.
4.31pmFormer Arsenal man Gervinho scored the winning goal for Ivory Coast against Japan. When asked about the threat that the winger poses, Colombia defender Cristian Zapata told reporters: "Sure, I have faced [him before]. [He is] fast and skilled. We have to stay focused, we are also fast and have our own qualities. Drogba's a beast inside the area. You have to stay focused throughout the match and mark very closely. We are a humble squad that knows how to win and does not suffer from overconfidence, we go step-by-step. We are mentally prepared to take the fight."
4.34pmIn his pre-match press conference, Ivory Coast manager Sabri Lamouchi said that his team need to do better: "The players are very happy with the victory [over Japan], but we are far from being qualified. We did not start very well in the game, conceding the first goal from a careless mistake."
4.38pmOnce again it looks like Colombia will have a good number of fans at the stadium for the game. Here's a picture from the team's Twitter feed of supporters making their way to their seats ahead of kickoff:
4.42pmWEATHER! It's a hot one in Brasilia this afternoon, with temperatures currently around 27C at the stadium. The good news is that humidity is low and there's no rain forecast, so it should be relatively comfortable conditions for the players.
4.45pmThis is just the first of three matches today. The other two sides in this group, Japan and Greece, meet later today. If there's a winner this afternoon, a draw between those two teams would result in the winner of this match securing their place in the knockout stage. In between the two Group C matches, England will face Uruguay, with both teams needing a win to keep themselves in contention in Group D. You'll be able to follow live updates from both of those matches with Sports Mole as well.
4.49pmPREDICTION! Before the players make their way out for the national anthems, it's time to make a prediction. After their first matches, there's a good chance that these two will be the teams to progress from Group C, but I think it will be Colombia who come out on top today, having looked pretty sharp up front against Greece. I'm going for a 2-1 win for the South Americans, although this tournament have proved impossible to predict so far!
4.53pmRight then, here come the players. It all looks pretty friendly between the two teams in the tunnel as they wait to make their way out, shaking hands and chatting to each other. You can be sure that will all stop when the game starts. Howard Webb leads them out.
4.56pmAs ever, it's that national anthems from both countries before the proceedings get underway. Colombia goes first and it become apparent just how many of their fans are in the stadium as their supporters belt out "Libertad y Orden".
4.59pmSerey Die is in floods of tears as the Ivorian national anthem is played. The African side don't have the same numbers of fans there as the Colombians, but those that have made the trip are certainly showing their support during the pre-match formalities.
1 minKICKOFF! Ivory Coast get the match underway.
2 minColombia are the early aggressors, winning the ball inside their own half before attempting a long ball forward which has just a little too much for Juan Cuadrado to reach. Rodriguez and Gutierrez try to link up on the edge of the box, but it's eventually cleared by the Ivory Coast.
5 minSouleymane Bamba launches the ball forward for Arthur Boka as the African side try to catch Colombia out on the counter-attack, but it goes out for a throw in. Gervinho tries a long ball into the box, but it harmlessly drops for Ospina. Both sides still seem to be sizing each other up and are yet to settle, but it looks like they're both keen to attack in the early stages.
8 minCHANCE! Cuadrado launches the ball forward to James Rodriguez, who backheels it perfectly for Gutierrez to unleash a volley from the edge of the box, but his finish goes wide of the post. It's a good move by the Colombians that was just lacking an accurate shot. Meanwhile, play has briefly been halted while a giant inflatable football is removed from the pitch. Rodriguez is eventually the one to pop it!
10 minCHANCE! Cuadrado makes a brilliant run down the right before trying to pull it back for Rodriguez, but Zokora makes the clearance. Gervinho tears down the other end of the counter and wins a corner for the Ivory Coast. This tempo of this match has gone up a notch or two in the last couple of minutes.
13 minIvory Coast win a free kick in a dangerous area. African Footballer of the Year Yaya Toure lines it up from just to the right of the penalty area, but it's nodded away by Yepes.
15 minCuadrado think he's through on the counter-attack for Colombia, but Boka catches him and forces him to put it behind for a goal kick. After a quiet opening five minutes, this match really has been end-to-end, although neither goalkeeper has really been tested yet.
18 minIvory Coast appear to be trying to slow things down as they patiently play the ball into Colombia's box before Toure has a cross cleared. Cuadradro, who really has been busy so far, bursts down the other end, but Barry is on hand to collect his cross in towards Rodriguez.
20 minThe Ivory Coast back four are just starting to get a little frustrated by Cuadrado, who has easily got the better of them so far. He's fouled twice, the second time giving Colombia a free kick 25 yards out. Rodriguez curls it into the box, but the flag is raised as Yepes and Boka clash while jumping for the ball, giving Ivory Coast the advantage.
23 minColombia have a corner, but Barry comes off his line to punch it away. Gervinho picks up the clearance and immediately looks to make his way down the other end. He has Toure in support, but he Man City midfielder trips, allowing the Colombia defence to steal the ball away from Gervinho.
26 minCHANCE! Ivory Coast are enjoying a good spell of possession but are struggling the penetrate the Colombia box. Ismael Tiote tries his look from range with a 25-yard drilled shot, but it was always rising and ends up in the stand behind the goal. He can hit them well from that range though, so it was well worth a go.
29 minCHANCE! How did he miss that?! Cuadrado launches a long ball forward for Rodriguez, who immediately pulls it back to an unmarked Teofilo Gutierrez, but the striker, who only had Barry to beat, completely mis-hits his shot, pulling it well wide. That's probably the best chance for either side so far.
32 minCHANCE! Ospina is called into action as Serge Aurier gets the better of Yepes with a couple of step-overs before slicing the ball towards goal, but the Monaco stopper manages to get down low to keep it out. Ivory Coast haven't had a great amount of time in their opponents box, but they do look dangerous when they get through.
34 minThere's a worrying moment for Ivory Coast as Yaya Toure is brought down by a solid but fair challenge from Sanchez. He eventually gets back to his feet but he's not moving all that well. With just over 10 minutes until half time, the African side will be hoping that he can walk it off, as he would be a huge loss this early in the match.
37 minCHANCE! Serey Die tries to curl the ball in from the edge of the box. It looks like he's hit it well, but it takes a deflection off a Colombian defender and goes behind for a corner, which Sanchez quickly clears. The good news for Ivory Coast through is that Yaya Toure appears to have shaken off the knock from a few minutes ago.
40 minBamba almost gifts Colombia a chance as he dispossesses Cuadrado on the edge of the box, but lets the ball bobble behind him before Gutierrez almost takes it back for the South Americans, but the defender eventually manages to clear. He hasn't looked at his sharpest so far this evening, and was lucky to dig himself out of trouble this time.
43 minCHANCE! Ivory Coast look to force an opening goal just before half time as Gervinho beats three defenders on the left of the box with some stunning footwork. His shot is blocked but it comes back for MAx Gradel, but he can't find a way through either. Colombia have done well to keep Wilfried Bony quiet so far, but Gervinho is proving trickier to handle.
45+1 minBony almost gets his chance as Gervinho carves his way through the Colombian defenders again, but Yepes gets it away to Rodriguez, but his cross goes behind for a goal kick, and that should be about it for the first half.
45+1 minHALF TIME: Colombia 0-0 Ivory Coast
5.51pmAn entertaining but goalless first half in Brasilia, where both sides have had chances but neither have broken the deadlock in this Group C clash.
5.54pmJuan Cuadrado and James Rodriguez have looked deadly for Colombia, but have lacked accuracy when in a goal-scoring position. Meanwhile, Gervinho looks sharp for Ivory Coast, but Wilfried Bony was pretty much anonymous throughout the opening 45 minutes.
5.58pmLet's looks at some of the stats from the opening 45 minutes. Ivory Coast just had the better of the possession with 53%, and also had more shots, with six compared to Colombia's four. Both sides had just the one shot on target. So far, it's been a relatively quiet evening for Howard Webb, with just 11 fouls in total and no bookings.
6.02pmYaya Toure took a knock shortly before the break but seemed to shake it off before the teams headed in. However, Ivory Coast must surely be considering bringing Didier Drogba on in the second half. They also have Salomon Kalou on the bench should they feel some extra fire power. Meanwhile, with Teofilo Gutierrez missing a sitter, Jackson Martinez may be hopeful of getting a run out before full time for Colombia.
6.04pmThe players are making their way back out for the second half. It doesn't look like either side have made any changes during the break.
46 minKICKOFF! Colombia get the second half underway.
48 minBamba continues his shaky performance from the first half as the back four pass the ball around for Ivory Coast, but a poor first touch from the right back almost lets Gutierrez in, but once again Bamba manages to salvage the situation.
49 minCHANCE! Ivory Coast win a free kick when Gervinho is tripped while sprinting towards the Colombia box. Toure goes directly for goal from the set piece, but Ospina manages to pat it away before taking hold of the ball.
51 minIvory Coast are looking lively at the start of this second half as Toure feeds the ball forward for Gervinho, but the winger can't control it in time and it goes behind for a goal kick.
53 minCHANCE! Colombia try to create a chance down the other end, but Boka hooks it away. Toure tries to create some space just outside the box, but is brought down by Aguilar, giving the African side a free kick. Toure elects to take it himself, but he doesn't get the shot right, curling it well wide.
54 minSUB! Colombia are forced into an early change as Victor Ibarbo appears to have picked up an injury, bringing Juan Quintera on for his first appearance of the tournament. James Rodriguez switches the the left hand side with Quintero taking over in the middle.
55 minBOOKING! Didier Zokora is the first player to be shown a yellow card this evening as he lunges into Cuadrado. It's a booking that will rule the defender out of Ivory Coast's final game of the group stage against Greece as he was also cautioned during their opener.
57 minCHANCE! Easily the best chance of the match so far for the Ivory Coast falls to Wilfried Bony as the striker is picked out with the fabulous ball in from Yaya Toure. Rather than taking a touch and unleashing his shot, Bony tries to hit it on the turn, as scuffs the ball behind.
58 minCHANCE! It's all Ivory Coast as the moment as Gradel quickly recovers it, but a well-timed tackle from captain Yepes clears the danger.
60 minOFF THE POST! Colombia respond to Ivory Coast's bright spell with a quick move down the other end. Cuadrado tries to slice it in but Barry tips it into the post before it goes behind for a corner.
60 minSUB! Before the corner, Ivory Coast make their first change, bringing on Didier Drogba in place of Wilfried Bony, who honestly hasn't been at his best today. Drogba immediately has an impact, heading the ball away from the Colombia corner.
63 minColombia press forward again as Rodriguez flicks the ball forward for Gutierrez. Bamba manages to tap it behind for a corner, but appears to have injured himself while doing so.
64 minGOAL! Colombia 1-0 Ivory Coast (James Rodriguez)
64 minA clinical header from James Rodriguez puts Colombia ahead as he loses his marker before nodding in from Cuadrado's corner delivery.
66 minIvory Coast immediately look to get themselves back on level terms. Gervinho passes to Drogba on the edge of the box, but the former Chelsea striker is tripped before he can get his shot away, giving the African side a good chance from a free kick.
69 minToure takes the free kick, but it's blocked by the wall. Ivory Coast win it back resulting in a shot for Auerier, but Ospina manager to tip it wide for a corner. Ivory Coast have certainly responded well to Rodriguez's goal!
70 minGOAL! Colombia 2-0 Ivory Coast (Juan Quintero)
70 minA poor corner from Ivory Coast allows Colombia to get on the counter, with Rodriguez bursting down the other end before sliding the ball forward for Juan Quintero, who has just Barry to beat. He fires the ball in low to score his first international goal and double the South Americans' lead.
72 minSUB! Colombia are making another change as Pablo Armero is replaced by Santiago Arias.
73 minSUB! Ivory Coast make their final change sending on Mathis Bolly in place of Serey Die.
74 minGOAL! Colombia 2-1 Ivory Coast (Gervinho)
74 minGervinho has threatened all evening and scores a fantastic goal to get Ivory Coast back into the tie. He collects the ball out wide before getting the better of two defenders and firing into the back of the net. Ospina got a hand to the ball, but couldn't keep it out. This should be a cracking final 15 minutes!
76 minIvory Coast are looking for the equaliser as Aurier curls the ball in towards Drogba. Ospina is taking no chances though and he punches it away before the striker can get a head to the ball.
78 minCHANCE! Boka fires in a dangerous looking ball towards Drogba, but the forward can't quite reach the ball for what would have been a simple tap in.
79 minSUB! Colombia make their third substitution, replacing Abel Aguilar with Alexander Mejia.
83 minColombia are really being tested as Ivory Coast desperately try to get back on level terms. Such has been their dominance in the last 10 minutes, if they got one back now, you would rule out them going on to get the win. Auerier fires it in for Drogba again, but Ospina quickly claims it. The keeper could have done better during Gervinho's goal, but has been decisive since to keep Ivory Coast's shots to a minimum.
85 minCHANCE! Salomon Kalou hasn't really seen much of the ball since he came on but he manages to get a shot away, but it lacked power and is easily gathered by Ospina.
87 minThere's a worry for Colombia as captain Mario Yepes appears to be in quite a bit of pain with an apparent knee injury. Colombia have used all of their substitutions so they'll be down to 10 men if he's unable to battle through the last few minutes. It looks like he's going to try to carry on through, but he's not moving brilliantly.
89 minAurier is brought down on the edge of the box on the right hand side. Toure takes what is basically a short corner, but he puts too much on the delivery and Tiote can't control it.
90+1 minBOOKING! Ismael Tiote gets the second yellow card of the game for a sliding challenge on Cuadrado. Meanwhile there will be four minutes of stoppage time.
90+3 minYepes, who still seems to be struggling a little, lets a ball slide through and Toure tries to rush in the tap it past Ospina, but the keeper manages to just beat him to it.
90+4 minYepes and Drogba battle for the ball on the edge of the box. The striker appears to win it but Howard Webb rules that the Colombia captain was fouled.
90+4 minFULL TIME: Colombia 2-1 Ivory Coast
6.57pmWhat a fantastic second half that was, more so for the Colombians as they manage to hold off a frantic push from the Ivory Coast to claim the 2-1 win. If Greece avoid defeat tonight, the South American side will be through to the next round.
6.59pmThe defeat does not mean Ivory Coast are out of the running by any means. A positive result against Greece in their final game of the group stage will give them a chance to progress as well.
7pmWell that's all from Brasilia for now, but stick around for reaction, analysis and player ratings from this match, as well as live coverage from the remaining two fixtures today. Our build-up for England's match against Uruguay is just getting underway, while Greece vs. Japan takes place later tonight. Thanks for joining me this evening, goodbye.