Bravo had earlier produced two fine blocks to deny Oscar Murillo and Miguel Borja as Colombia were struggled to break the deadlock.
Colombia’s Argentinian coach Jose Pekerman bemoaned a lack of precision in front of goal but was buoyed by the return of talismanic striker Radamel Falcao, who was introduced as a half-time substitute.
“We tried everything and we had chances but we lacked precision,” Pekerman said.
“But the most important fact of the game was the return of Falcao.”
In other games, Paraguay suffered a 4-1 mauling against Peru in Asuncion to derail their qualification campaign.
Paraguay took an early lead through Cristian Riveros after nine minutes but Peru hit back with second-half goals from Christian Ramos, Edison Flores, Christian Cueva and an Edgar Benitez own goal to run out convincing winners.
Paraguay coach Francisco Arce attempted to put a positive spin on his team’s loss.
“We’re still in the race to qualify,” Arce said. “We don’t think we’re dead, we just need to pick ourselves up and get on with it,” he added.
Paraguay, who are two points outside the qualifying positions, face Bolivia away in their next game.
Venezuela meanwhile scored their first win of the qualifiers with a 5-0 thrashing at home to Bolivia, with Josef Martinez scoring a hat-trick.