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Bernardo Silva fired in a superb strike in the 79th minute but Villa players immediately protested to the referee.
In the build-up, Rodri was quite clearly in an offside position as Silva headed the ball forwards but he was deemed to be active again after Tyrone Mings controlled the ball.
BT Sport's Peter Walton had first thought the goal should have been chalked off as he believed Rodri intereferred, yet the feeling from the officials, with the help of VAR, was that offside became irrelevant as soon as Mings made the touch.
His chest control was wayward and allowed Spain international Rodri to nip in and set up Silva for a brilliant opener.
Still, some fans weren't quite having it:
Villa manager Dean Smith was sent off for his reaction to John Moss' decision.
Ilkay Gundogan sealed the win with a stoppage time penalty after Matty Cash handled Gabriel Jesus' headed effort.