The Barcelona man capitalised on Ospina's error to equalise in the second-half, before providing the impetus for El Kun to wrap up a fortuitous three points
The win, however, fails to clear the doubts circling around Alejandro Sabella's charges, who until the equaliser struggled greatly against their rivals who were missing Radamel Falcao and Fredy Guarin amongst other first-teamers.
Despite the intense heat inside the Estadio Metropolitano, both teams came out at a high pace, especially the Colombians who attacked with great earnest but little precision down the flanks. Argentina, meanwhile, played far too conservatively, and seemed dependent on a moment of magic from Messi to generate danger.
Rival No. 10 James Rodriguez had the only chance of a scrappy first 20 minutes, firing in a low, long-range effort that caused Sergio Romero little trouble. As the game progressed, however, the home side started to assert themselves more, with Adrian Ramos and Pablo Armero in particular stretching their opponents down the flanks.
A wonderful run from Ramos almost led to danger for the Albiceleste, but the Hertha man was unlucky to see his effort deflect off Nicolas Burdisso and away from danger. The half took a decisive turn, however, when a nasty challenge from the Roma defender led to his own injury withdrawal from the field.
Leandro Desabato was the chosen replacement, while the Colombians almost took advantage of their temporary numerical superiority when Armero found Jackson Martinez free in the box; only for the striker to make a complete hash of his header. Just before half-time, and with Argentina hanging to go in level, the Cafeteros delivered a hammer blow.
An enterprising run from James earned a free-kick on the edge of the area, and Dorlan Pabon's driven effort took a wicked deflection off Javier Mascherano to finish in the back of the net. The goal was the final action of the half, sending Argentina into the dressing room dejected and seemingly without ideas how to approach the opposition area.
Alejandro Sabella gambled on a more attacking line-up for the second period, sending on Sergio Aguero to galvanise the ponderous Argentine play of the first 45. It was Colombia who were back on the front foot, however, as James tested Romero from deep seconds after the whistle had blown. There was more attacking intent from the visitors, and only a last-minute intervention from the excellent Abel Aguilar prevented Gonzalo Higuain from breaking through.
The equaliser arrived right on the hour-mark. Lionel Messi did well to open up the game in the Colombian final third, and after David Ospina spilled Jose Sosa's low cross Messi swooped to flick the ball into the empty net.
The goal lifted the Albiceleste, who for a spell finally seemed to click as the Colombians struggled to come to terms with their setback. Aguero tried his luck from deep after another fluid move, but Ospina this time held well to end the danger.
The home side were ragged, misplacing pass after pass and inviting their rivals to stream forward as they had not done earlier in the fixture. Argentina, however, still lacked a cutting edge in front of goal, and only looked capable of breaking through when Messi was directing play. Indeed, Colombia almost took back the lead when Camilo Zuniga blasted through the defence, but his shot was saved at point-blank range by Romero.
Six minutes from time Argentina swooped to claim a fortuitous victory. Messi this time was creator, leaving Mario Yepes stranded to thread the ball through to Higuain. The Real Madrid man's shot was saved well by Ospina, but Sergio Aguero was on hand to slot home the rebound and silence the Barranquilla crowd.
The win puts Argentina into joint first-place in the Conmebol World Cup qualifying standings, although Uruguay have a game in hand over their neighbours. Colombia meanwhile stay on four points after their first three games.