The Monaco's man strike has guaranteed Jose Pekerman's men at least a play-off spot for Brazil 2014, with the visitors missing a penalty
Colombia have all but confirmed their place at World Cup 2014 following James Rodriguez's strike against 10-man Ecuador.
An early red card to defender Gabriel Achilier changed the match with Rodriguez scoring the only goal of the game for the hosts, finishing off Monaco team-mate Radamel Falcao's parried shot.
But Ecuador missed a golden opportunity to equalise in the second half with captain Walter Ayovi firing his penalty wide of the target.
It was a free-flowing contest early with Ecuador's Jefferson Montero having the first meaningful effort on goal as he stung the palms of Colombian goalkeeper David Ospina from long range.
Falcao was gradually starting to work his way into the game and the France-based striker should have given Colombia the lead on 24 minutes when he headed Pablo Armero's chip straight at Ecuador goalkeeper Maximo Banguera from close range.
The match-defining moment came in the 28th minute when Ecuador central defender Achilier was given a straight red for dragging down Teo Gutierrez as the Colombian streamed through on goal with just the goalkeeper to beat.
Colombia made their advantage count just two minutes later as Falcao's long-range shot was parried by Banguera before Rodriguez rolled the ball into the net with the Ecuadorian shot-stopper sprawled on the ground.
There was a major delay in starting the second half with floodlight issues preventing play from resuming for 20 minutes as rain poured down.
With the man advantage, the Colombians dominated possession in the second-half but the away side had a golden opportunity to level the contest just after the hour mark.
After Manchester United winger Antonio Valencia was fouled in the penalty area, Ayovi stepped up to give Ecuador a chance of stealing a result but inexplicably curled his penalty wide with Colombia's goalkeeper diving in the other direction.
Barely a minute later, Gutierrez should have doubled the hosts' lead but somehow chested the ball against the post from point-blank range, although it mattered little as the home side held on for victory.
Both Argentina and Colombia are all but assured their place at next year's showpiece but Ecuador remain in third, five points clear of the fifth-place play-off position occupied by Uruguay.