Rooney opened the scoring with an early penalty and Danny Welbeck increased United's lead before half-time.
England forward Rooney bagged his 31st goal of the season in the second half before Nani's late goal sealed a crucial victory.
Thanks to Rooney's brace, Sir Alex Ferguson's men were able to reestablish a significant lead over title rivals Manchester City with four games left to play.
After their shock midweek defeat at Wigan, and City's 6-1 demolition of Norwich on Saturday, this was the perfect response from United.
"Wednesday was a blip, we just didn't turn up but today we put in a good performance," said United defender Rio Ferdinand.
"We weren't thinking about City's result. The pressure is always on us, from within, from the fans, the manager, the pressure to win is always there.
"We played some good football today with some nice one-touch football. We want to win every game. We don't care where we win the title -- it could be in the garden, as long as we win it."
Sunday's win, however, came laced with controversy.
Last Sunday, United winger Ashley Young earned a penalty and got QPR's Shaun Derry sent off in process when he fell under minimal contact from the midfielder in a 2-0 win.
And the England international was involved in another controversial incident against Villa when he appeared to exaggerate his fall after Ciaran Clark stuck out his leg in the penalty area in the seventh minute.
Referee Mark Halsey gave the penalty and Rooney calmly stroked home the spot-kick.
The champions increased their lead in the 43rd minute when Welbeck slid in to score after Villa defenders James Collins and Nathan Baker failed to clear Patrice Evra's low cross.
Rooney made it 3-0 when his close-range effort deflected in off Collins in the 73rd minute and Portugal winger Nani concluded an emphatic victory with the fourth goal in stoppage-time.