A first-half goal by Monaco striker James Rodriguez secured all three points for the Colombians, who are now guaranteed at least a play-off spot from South America's nine-team qualifying competition.
The victory put Jose Pekerman's team level with Argentina on 26 points at the top of the standings and both sides could even book their places at next year's finals in Brazil later Friday if other results go their way.
A pre-match deluge at Barranquilla's Estadio Metropolitano had appeared to leave the game in jeopardy at one point, with parts of the field covered in large pools of water as the rain tumbled down. However the stadium ground staff worked ferociously to clear the excess water and after a 90-minute delay, Brazilian referee Heber Lopes got proceedings under way.
A lacklustre opening period saw neither side manage to gain control of the contest, and it was Ecuador who went closest to scoring when Jefferson Montero's swerving shot effort was punched away by Colombia goalkeeper David Ospina in the 18th minute.
But the complexion of the game changed decisively on the half-hour mark when Ecuador were reduced to ten men, Achilier sent off for bringing down Colombia's Teofilo Gutierrez as he sprinted clear on goal. The dismissal seemed to energise the Colombians and within a minute they had taken the lead through Monaco youngster Rodriguez.
Monaco mates give Colombia early lead
Monaco team-mate Radamel Falcao - named in the starting line-up after recovering from an ankle injury - unleashed a ferocious long-range effort which Ecuador's stand-in keeper Maximo Banguera could only parry away.
The rebound fell kindly to Rodriguez who rifled home an angled low shot to put Colombia 1-0 up heading into the half-time break.
A floodlight blackout then delayed the start of the second half for 15 minutes, and there was a further interruption soon after the restart when Colombia keeper Ospina received medical attention for several minutes after a heavy blow to the head.
Ecuador were then presented with a golden chance to get back on level terms when Colombia defender Carlos Sanchez hauled down Manchester United winger Antonio Valencia in the box on 61 minutes. But Ayovi miscued his spotkick horribly and Colombia escaped to claim a win which puts them within touching distance of a first FIFA World Cup since their appearance at the France finals 15 years ago.