Alisson was shown a red card after 25 minutes for a fierce tackle and another in stoppage time
The result means Ecuador have one point from two games in Group B and Venezuela have two points from three.
Captain Casemiro said Brazil fully deserved the three points.
A late header from Edinson Cavani gave Uruguay a 1-0 win over Copa America holders Chile which saw them snatch top spot in Group C at their opponents' expense and set up a quarter-final meeting with Peru.
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