Lionel Messi then saw his looping effort strike the frame of the visitors' goal before being denied by Muslera from a free kick.
Uruguay created precious little in the first half and the second half did not see the visitors improve.
Ezequiel Garay came close to giving Argentina the lead just two minutes into the second half when he had the Uruguay goal at his mercy, with Gonzalo Higuain and Sergio Aguero trying their luck in vain as the match wore on.
The hosts eventually broke the deadlock in the 66th minute, with Messi and Di Maria combining well before the Barcelona forward slotted home the Real Madrid winger's intelligent pass.
The duo again combined for Argentina's second in the 75th minute, Aguero putting the ball into the Uruguay goal with ease after being nicely teed up by Di Maria.
Messi added the cherry on the cake five minutes later when he scored from a free kick.
The win in Mendoza means that Argentina remain at the top of the CONMEBOL standings with 17 points from eight matches.