The victory kept the 1978 and 1986 world champions on top of the nine-nation South American group, while continental champions Uruguay remain in the fourth and final automatic qualifying place.
He opened the scoring in the 66th minute when he slid in from a cross by Angel Di Maria with his second goal – and his team’s third – coming eight minutes from time.
In between, Manchester City’s Sergio Aguero hit the target, again from good approach work from the tireless Di Maria.
Argentina thought they had a fourth goal in the dying minutes but substitute Hernan Barcos’s effort, off a one-two with Messi, was ruled out for offside.
The win leaves Argentina with 17 points from eight matches, one ahead of Colombia and Ecuador who both also won on Friday.
“When you give everything, the results are easier,” said Messi. “This victory leaves us very happy because we played a team which is very strong. Now comes a tough game against Chile (on Tuesday). Even though they lost today they are rivals whom we respect.”