The two goals he scored in this game brought his total in the current World Cup qualifying campaign to six goals in eight games, the most he had scored in a qualifying campaign.
He had scored just four goals in 18 qualifying matches on the way to the 2010 World Cup
Messi scored Argentina's first goal in the 66th minute, after a highly spirited Uruguay held on for a goalless first half.
Uruguay, who had rolled into town with an attacking triple threat of Edison Cavani, Luis Suarez and Diego Forlan, were always a threat as they did not shy away from attacking the home side.
Sergio Aguero scored the second for Argentina in the 75th minute, before Messi wrapped up a hugely successful night for Argentina with five minutes left to play.
The win lifted Argentina to the top of the South American qualifying table with 18 points, one more than Colombia.
Uruguay, with 12 points, are still in qualifying place, but only just. They are tied on points with Chile, with only goals difference keeping them ahead.