Much had been made during the build-up of a planned protest, with a plane carrying the message "Wrong One - Moyes Out" flying over Old Trafford shortly after kickoff.
However, Rooney's brace against the Villans, plus goals from Juan Mata - the Spaniard's first since his January move from Chelsea - and Javier Hernandez earned United a victory to take some of the pressure off Moyes.
Rooney told BT Sport after the match: "Today was a big game for us after midweek.
"We had to respond and it was difficult. We had a slow start, going behind, but we came through it and got the win and deserved it. It was a good win for us.
"We know the support the manager has got from the players and from the fans and that's what matters. The support he got from the fans was incredible again today."
United's next fixture is against Bundesliga winners Bayern Munich in the Champions League at Old Trafford on Tuesday.