The first half was played at a lightning-fast pace but remained scoreless as both sides' strikers struggled.
Colombia was first to break through in the 64th minute, as James Rodriguez jumped highest after a Juan Cuadrado corner and headed the ball into the net.
Six minutes later they were up 2-0 after a Serey Die giveaway led to an easy goal for Juan Quintero.
Ivory Coast kept attacking and wound up with the best goal of the match, a solo effort by Gervinho in the 73rd minute. With the ball on his feet at the sideline, he darted in and beat three men and then the keeper.
But despite more Ivory Coast pressure, a second goal would not come and Colombia hung on.