Elias got the goal that gave the 2012 champions the three points in a match that was played behind closed doors after San Lorenzo were punished for fans who lit fireworks inside their stadium during last year's final.
However, the home side had the best chances and were aggrieved at what they said were provocations by their Brazilian opposition after the final whistle.
Several Argentines went after their opponents as the players made their way to the tunnel and scuffles ensued before other players and police calmed the situation.
The result leaves Corinthians top of Group Two with six points. San Lorenzo and Sao Paulo are tied in second place with three, with Uruguayan side Danubio pointless.
It was a successful night for another Brazilian team as Internacional came from behind in Porto Alegre to beat Ecuador's Emelec 3-2.
The result means the two sides are now tied at the top of Group Four with six points from three games.
Bolivia's The Strongest have three and play last-placed Universidad de Chile on Thursday.
In Wednesday's other Libertadores game, Colo-Colo of Chile beat Mexican side Atlas 2-0.
(Reporting by Andrew Downie; Editing by Greg Stutchbury)
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