Rooney found the target in the 53rd and 70th minutes with cool finishes, after Cristiano Ronaldo - with his 35th goal of the season - and Carlos Tevez had also scored.
United boss Sir Alex Ferguson said: "I thought Wayne was never going to score, to be honest.
"But he is the kind of striker who could go on a run now and get goals in his next six or seven matches."
United never looked back and got the result they craved following Arsenal's dramatic victory at Bolton earlier in the day.
Ferguson said: "It was only when I saw the replay I realised what Ronaldo had done.
"The execution was absolutely brilliant, so full marks to him.
"We displayed some great attacking movements, and you have to admire the players' enthusiasm in difficult conditions.
"It has to be one of our best performances of the season and just what was needed after Arsenal's victory.
"We have six games to go, four of them away, and it will be nip and tuck. But we are playing well and have improved our goal difference."
Villa manager Martin O'Neill was gracious in defeat - the club have not won at the ground since 1983.
He said: "I thought United were really brilliant. They have been in these situations many times, in the Champions League quarter-finals and going for the title.
"Their enthusiasm, determination and ability are there for all to see. They are a class side, no question of that.
"Many teams would have struggled like we did.
"We have real distance to go, we know that. That [United's level] is what we have to aspire to.
"Aston Villa are capable of getting in there. However, we have to start getting back to winning ways."