The South American side moves into first place in Group C after a match that opened up in the second half.
Colombia has maintained its perfect record in World Cup Group C with a dramatic 2-1 win over Cote d'Ivoire.
Following a first half that was low on goalmouth action, the match burst into life in the final 30 minutes.
James Rodriguez set the ball rolling with a powerful header from a Juan Cuadrado corner in the 64th minute, before Juan Quintero doubled the advantage six minutes later.
Gervinho pulled one back for Cote d'Ivoire 17 minutes from time, but it proved to be mere consolation for the African outfit.
Ivory Coast created a number of late chances but Colombia captain Mario Yepes, playing in his 100th international match, was supreme throughout, repelling everything thrown at him.
The result sends Colombia three points clear at the top of the group, and the team will be assured of its place in the second round if Greece fails to beat Japan later in Thursday's action.PHOTOS: Beautiful people in Brazil | Brazil protests | Soccer fanatics | Fan tattoos
The unchanged Colombians had the better of the early chances, with Teofilo Gutierrez sending a half-volley wide of the right-hand post from the edge of the penalty area.
The Ivorians, meanwhile, were struggling to get the likes of Wilfried Bony, Gervinho and Max Gradel into the game, though Cheick Tiote drilled over the crossbar 25 minutes in as they got a rare sight of goal.
The best chance of the opening period came for the South Americans three minutes later.
Gutierrez found himself in acres of space in the center of the Ivorian box, but could only scuff clumsily wide of the left-hand upright when he was delivered the ball on a plate by Rodriguez.
Serge Aurier's low drive at the other end forced goalkeeper David Ospina into a diving save shortly after the half-hour mark, before Gradel went down in the area in search of a penalty under the challenge of Cristian Zapata.
Howard Webb – refereeing his first World Cup match since the 2010 final – was having none of it.
Victor Ibarbo failed to get the ball out from under his feet as he tried to set up a shooting angle at the beginning of the second half, before Yaya Toure curled a free kick well wide of the target at the other end from a promising position.
Didier Zokora then surrendered his place in Tuesday’s meeting with Greece by picking up a booking for a clumsy challenge on Cuadrado.
The Fiorentina man came agonizingly close to putting Colombia in front on the hour, firing an effort across goal only to see it touched onto the post by Boubacar Barry.
Barry was not so fortunate next time, however, as his touch was not enough to keep out Rodriguez’s powerful header from a Cuadrado corner.
And the match appeared to be all but won six minutes later as Quintero found the space to slot beyond Barry.
However, Cote d'Ivoire was right back in it in the 74th minute when Gervinho burst into the box to power an effort into the back of the net, with Ospina unable to keep the effort out despite getting a glove to the ball.
It would prove to be the Africans' only goal of the encounter, leaving them sweating on a place in the next round, with Greece to face in their final group fixture.
Colombia's last match will be against Japan, but it may already be through by then.