Messi struck with a stunning free-kick in the 10th minute before setting up Lucas Pratto for a first-half header at the Estadio San Juan del Bicentenario on Tuesday
The five-time Ballon d'Or winner was a constant threat for Edgardo Bauza's team, who desperately needed their win following a difficult recent period, and set up Angel Di Maria for a tap in for the sealer late on.
Radamel Falcao had a couple of first-half chances for Colombia, but they were otherwise outplayed.
The result meant Argentina moved above Colombia in CONMEBOL qualifying, a huge boost following losses to Paraguay and Brazil.
Bauza made three changes to his team comprehensively beaten by Brazil, Pablo Zabaleta, Enzo Perez and Gonzalo Higuain making way for Gabriel Mercado, Ever Banega and Pratto.
Colombia made numerous changes to the team that held Chile last time out, including welcoming back Juan Cuadrado and starting Falcao.
It was the hosts who started the better, and Nicolas Otamendi headed a Messi free-kick over the bar in the sixth minute.
Falcao had a tough chance just two minutes later before Messi opened the scoring in sublime fashion.
The Barcelona star gave David Ospina no chance, his 25-yard effort curling away from the goalkeeper and in off the crossbar.
Falcao almost equalised for Colombia in the 19th minute, only to send his powerful header from a James Rodriguez free-kick over the bar.
His team would be punished for the miss, more Messi brilliance seeing Argentina 2-0 up as his chipped pass found Pratto to head into the bottom corner in the 23rd minute.
Di Maria went close with a volley after the break before blasting an effort against the post from an angle following a Messi pass.
Argentina seemed more content to sit back in the second half and the visitors struggled to break them down, while looking vulnerable on the counter-attack.
They would seal the points in the 84th minute, again thanks to Messi.
Messi won the ball in the corner before racing into the area, cutting back for Di Maria to put a finish into the roof of the net and secure victory.