Messi, given more room in the second half when coach Alejandro Sabella put Aguero on for midfielder Pablo Guinazu, levelled the scores just past the hour.
Colombia had taken the lead on the stroke of half-time when midfielder Darlon Pabon's free-kick was deflected by Javier Mascherano past goalkeeper Sergio Romero.
The win at the Metropolitano in steamy Barranquilla puts Argentina level on seven points with Uruguay although the South American champions, who did not play on Tuesday, have a match in hand.
"We wanted our revenge more than anything because of what happened with Bolivia. I think we won because we went out convinced we can beat anyone despite [Friday's result]," Aguero told a TV reporter on the pitch.
Argentina began the match cautiously having suffered heavy criticism following their 1-0 loss away to Venezuela last month and Friday's 1-1 draw with Bolivia in Buenos Aires.
Colombia deservedly took the lead on the stroke of half-time when winger Dorlan Pabon's low free-kick took a deflection on Javier Mascherano and wrong footed goalkeeper Sergio Romero. Pablo Zabaleta had given away the free-kick for a foul on midfielder James Rodriguez on the edge of the box.
Messi was at the hub of Argentina's two scoring moves, grabbing the first in the 61st minute when poked home a loose ball from a tight angle after Colombia goalkeeper David Ospina failed to hold on to Argentina midfielder Jose Sosa's low cross.
The winner came from another move started by Messi, who fed Gonzalo Higuain in the box and the striker's low shot to the corner was parried by the diving Ospina with Aguero steering the loose ball inside the base of the post.
The home side had the better of the first half as Argentina got bogged down trying to work their way through a tight home defence with short passes, whereas Colombia used the width of the pitch to attack down the flanks through full-backs Pablo Armero and Camilo Zuniga.
The twice world champions lost central defender Nicolas Burdisso to a knee injury in the 34th minute.
Burdisso went in badly on Rodriguez and looked set for at least a yellow card but it quickly became clear he had done his knee serious damage and referee turned his attention to getting the defender treated and replaced.
"In the first half we controlled the ball [but] maybe we lacked some clarity, but we were facing a great team and terrible heat," said Argentina midfielder Rodrigo Brana of the humid conditions in heat above 30 degrees in Barranquilla on the Caribbean coast.
"When you're not doing well it's not bad to start adding [points], but in Argentina you're always obliged to give a little more," he told reporters.
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