Japan, Greece fail to find net][Read: Uruguay beat England 2-1]
The South American side scored twice in six minutes in the second half after coming very close to scoring a couple of times to seal the win and almost ensure a second round berth.
With this win, Colombia have six points from two matches
The first goal came from James Rodriguez's powerful header from a corner in the 64th minute while substitute Juan Quintero made a low finish in the 70th minute in front of 68,000-plus spectators comprising mostly supporters of Colombia.
Gervinho reduced the gap within three minutes of Colombia's second goal when Gervinho scored on the run but Ivory Coast, who beat Japan in their first match, could not find the equalizer.
Colombia require a point now to enter the second round, the first time since 1990.
Japan and Greece will play in the other Group C match scheduled in Thursday.