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.
"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."
In-form Falcao shines for Colombia
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."
Paraguay's fifth successive defeat left them firmly rooted to the foot of the table.
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.
Their miserable night was completed by having Pablo Contreras and Arturo Vidal red-carded.
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.