The win moves Argentina level with Paraguay on four points at the top of Group B, and they will reach the knockout stages with a draw from their final game against Jamaica.
However, Uruguay wasted the best chance of the first half when Diego Godin somehow managed to head wide after being left unmarked in the box.
Argentina continued to ask questions at the other end of the pitch, with Muslera denying Aguero and Messi heading wide, before Martino was sent to the stands after angrily confronting one of the officials.
Uruguay started the second half well, but they were behind 11 minutes after the break when Pablo Zabaleta delivered the perfect cross for Aguero to head home at the front post.
Messi, Aguero and Di Maria were all constant threats to the Uruguayan defence, but Argentina looked vulnerable at the back, too, and they almost conceded an equaliser when Diego Rolan fired over after collecting a loose ball in the box.
Alvaro Gonzalez then came close for Uruguay with a 30-yard volley which drifted over, before the impressive Muslera kept out a low strike from Messi.
Despite being forced to survive pressure in the closing stages, Argentina held on for a win which puts them in a strong position to top Group B.