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.
Messi grabbed his 11th and 12th goals of the campaign in Mendoza, but the Argentina skipper had to wait until midway through the second half to unlock a tight Uruguay defence.
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 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.”
Colombia, coached by veteran Argentine Jose Pekerman, moved to 16 points with a 2-0 home win over Paraguay in Barranquilla with both goals coming from prolific Atletico Madrid striker Radamel Falcao.
He opened the scoring after 52 minutes and closed out a memorable performance with a second, two minutes from time.
“Undoubtedly Paraguay are a strong team, we knew it would be difficult, and in the end we got the goals that gave us the victory,” said Falcao.
“But there is still a long way to go to the World Cup finals.”
Colombia have now won their last three qualifiers — beating Uruguay 4-0 and Chile 3-1 before Friday’s triumph.
Paraguay’s fifth successive defeat left them firmly rooted to the foot of the table.
Ecuador also stayed on course for the finals with a 3-1 win over Chile who finished with nine men in Quito.
Felipe Caicedo scored twice for Ecuador with a 33rd-minute opener followed by a 56th-minute penalty while Segundo Castillo added the third in stoppage time as Ecuador claimed a fifth successive home win.
Chile, who have never won in the Ecuador capital, had taken the lead through a Juan Carlos Paredes own-goal in the 25th minute.
Their miserable night was completed by having Pablo Contreras and Arturo Vidal red-carded.
In La Paz, Bolivia and Peru fought out a 1-1 draw which did neither side any favours in their faltering campaigns.
The top four teams in the South American qualifying tournament will be guaranteed spots in the 2014 finals with the fifth-placed team playing off against the fifth-best side in Asia.