Mexico took the lead in the fifth minute when winger Alexis Vega scored a penalty after Luis Diaz brought down Uriel Antuna inside the box and Gerardo Arteaga made it 2-0 after finishing off a team move in the 28th minute.
Colombia hit back after the break, with Sinisterra heading home in the 48th minute and scoring again three minutes later.
Barrios then completed Colombia's comeback with a brilliant volley in the 67th minute.
The referee paused the match in the 82nd minute because of anti-gay chanting in the crowd.
Colombia failed to qualify for the World Cup.