The victory means Colombia are guaranteed at least an intercontinental play-off berth against an Asian nation - a prize for the fifth-place finisher in the nine-team group - with three rounds to go.
They will be hoping to advance automatically, though, despite struggling to get the better of an Ecuador side who played for over an hour with 10 men following Gabriel Achilier's red card for a crude lunge at Teofilo Gutierrez.
Achilier might argue the pre-match storm which delayed kick-off for two hours in Barranquilla was a contributing factor but Colombia were unforgiving and took the lead within four minutes of his departure.
Monaco striker Radamel Falcao fired in a shot which Ecuador goalkeeper Maximo Banguera could only parry into the path of James Rodriguez, another Monaco man, and he slotted home.
Colombia peppered the Ecuador goal in search of a second goal but found Banguera in excellent form.
The visitors ought to have equalised on the hour mark when Carlos Sanchez fouled Antonio Valencia inside the area. Walter Ayovi took the spot-kick but screwed his effort wide of goal.
Ecuador dropped to fourth after Chile thrashed Venezuela 3-0. Eduardo Vargas put Chile ahead after 10 minutes and Marcos Gonzalez doubled their advantage 20 minutes later. Impressive Juventus midfielder Arturo Vidal made it 3-0 with five minutes to go.
Luis Suarez scored twice as fifth-placed Uruguay won 2-1 in Peru.
The Liverpool striker, currently banned from playing for his club side after biting Chelsea's Branislav Ivanovic in a Premier League fixture in April, opened the scoring from the spot after being felled by Christian Ramos after 43 minutes.
Suarez was again at the centre of controversy two minutes later when he was fouled from behind by Josepmir Ballon. Victor Yotun waded in needlessly, suggesting Suarez had gone to ground too easily, and was sent off after a brief melee.
Suarez exacted full revenge after 66 minutes with a wonderful second before Schalke winger Jefferson Farfan netted a late consolation with a fine free-kick.
Paraguay kept alive their faint hopes of qualification with a 4-0 thrashing of Bolivia - Jonathan Fabbro, Roque Santa Cruz, Richard Ortiz and Gustavo Gomez grabbing the goals.
On Tuesday, Uruguay meet Colombia, Venezuela host Peru, Argentina visit Paraguay and Bolivia take on Ecuador.