English Premier League star Aguero headed home a cross from Manchester City team-mate Pablo Zabaleta in the 56th minute to settle a gritty encounter that leaves the Argentines on pole to win Group B.
Uruguay's defeat means the 2011 champions must now beat Paraguay in their final group game to be certain of clinching a place in the last eight, although they could still reach the knockout rounds as one of the best third placed teams.
A tense first half had seen Argentina, surprisingly held to a 2-2 draw by Paraguay in their opening game, dominate possession and territory but fail to break down a resolute Uruguayan defence.
The two best chances of the opening period both fell to Argentina, with Manchester United winger Angel Di Maria testing Fernando Muslera in the ninth minute with an angled shot that the Uruguayan goalkeeper needed two attempts to gather.
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Muslera was pressed into action again midway through the half, producing a superb one-handed save to deny Aguero after the striker met Lionel Messi's sublime cross with a downward header.
On the stroke of half-time tempers flared once more with Argentina enforcer Javier Mascherano booked for sliding through Uruguay playmaker Nicolas Lodeiro, who had earlier seen yellow for a wild challenge on Zabaleta.
Uruguay carved out their best effort in the opening minutes of the second half, Maxi Pereira uncorking a fierce shot that Argentina goalkeeper Sergio Romero did well to clear.
With Messi being shadowed at every turn, it fell to others to break the deadlock and the game-changing moment came courtesy of Javier Pastore on 56 minutes.