Messi scored first from the penalty spot in the ninth minute of the game in the Argentine city of San Juan, before providing assists in the 23rd minute and 84th, for goals to Lucas Pratto and Angel Di Maria respectively.
The win means the Albiceleste move to fifth position in South American qualifying, with 19 points.
The top four teams qualify automatically for the finals in Russia, while the fifth-placed team goes into a playoff against a side from another region.
Elsewhere in South American qualifying, Brazil managed a comfortable 2-0 win over Peru to hold their position at the top of the group, while Chile defeated Uruguay 3-1. Ecuador defeated Venezuela 3-0 at home, and Bolivia beat Paraguay 1-0,