Christian Benteke squandered a number of goalscoring opportunities for the hosts before Colombia striker Radamel Falcao broke the deadlock six minutes into the second half.
Victor Ibarbo then added a second with a powerful left-footed volley in the 66th minute, but the Belgians had no response.
The defeat is Belgium’s first for exactly a year - their last reverse coming in a 2-1 loss to Romania on November 14 2012 - while Colombia have now won five of their last seven.
Benteke had the first effort at goal for the hosts in the sixth minute, but directed his header narrowly wide of 42-year-old keeper Faryd Mondragon’s right post from close range.
Mondragon's opposite number Simon Mignolet then needed to be alert 10 minutes later as he touched the ball behind for a corner after Falcao failed to make a meaningful connection with a dangerous cross from the right.
And Jose Pekerman's men doubled their advantage six minutes after the hour mark as substitute Ibarbo brought the ball down superbly 12 yards out before firing a left-footed volley beyond Mignolet shortly after being introduced to the action.
Moments later, Dries Mertens did brilliantly to knock the ball between two defenders, but his eventual effort was thwarted by the same post that had denied Fellaini as Wilmots' side's nine-game unbeaten run came to an end.
