Aguero met a 56th-minute cross from his Manchester City team mate Pablo Zabaleta and buried an unstoppable effort past Uruguayan goalkeeper Fernando Muslera at his front post.
Argentina coach Gerardo Martino was banished to the stands for arguing with the match officials after just half an hour of a stormy encounter which frequently threatened to boil over.
The result left Argentina and Paraguay level at the top of Group B with four points each, ahead of Uruguay on three.
Jamaica, who lost 1-0 to Paraguay earlier in the day, are bottom without a point ahead of the final round of group matches on Saturday.
The Argentines took the game to their opponents from the start and Aguero almost gave them the lead with a header from a Lionel Messi cross after 25 minutes, forcing a fine reflex save from Muslera.
Uruguay made a more cautious start but had their chances too, Diego Godin heading just over towards the end of the half.
The atmosphere was tense and when Martino jumped from the bench to remonstrate with the match officials, the Brazilian referee sent him off. He spent the rest of the match watching through a window, high in the stands.
Eleven minutes after the break, Aguero made the breakthrough.
Javier Pastore started the move with some trickery in midfield before threading the ball down the right wing for Zabaleta, who crossed into the box for Aguero to score.
The Uruguayans finally came out of their shell and had their chances to equalise.
Striker Diego Rolan squandered their best opportunity on 75 minutes, scooping the ball over from six yards after goalkeeper Sergio Romero had parried Alvaro Pereira's stinging shot.
Argentina face Jamaica in their final group match in Vina del Mar on Saturday while defending champions Uruguay stay in La Serena to take on Paraguay in a repeat of the last Copa America final in 2011.
(Writing by Gideon Long; Editing by Peter Rutherford)
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