Rooney maintains unbeaten run
United, who barely spent a penny as their rivals splashed out more than 200 million pounds in a bid to match their consistency, move to 54 points and stay five clear.
Arsenal are second with 49 after they fought back to beat Everton 2-1 at Emirates Stadium while fourth-placed Chelsea won 4-2 at Sunderland to make it three league wins in a row.
The champions are now on 44 points and just a point behind Manchester City, who visit Birmingham City on Wednesday.
The night's other game was a 2-2 relegation thriller between West Bromwich Albion and Wigan Athletic.
A year ago England striker Rooney was the hottest property in the game as everything he touched turned to goals but he has never been able to regain that form after an injury last March.
He had a forgettable World Cup and a flat first half of the season for United, with the diversion of his shock transfer demand and quick change of mind adding to the pressure.
In recent weeks, though, he has begun to show signs of his former sharpness and he certainly hit the ground running on Tuesday when he netted 50 seconds after kick-off.
He brought down a clearance from United goalkeeper Edwin van der Sar and sent a dipping shot just under the bar from the edge of the box - then doubled the lead with a tap-in from a perfect Nani cross at the end of the half.
"It was a marvellous early goal. It was great vision from Edwin but what a finish - a marvellous finish," United manager Sir Alex Ferguson told Sky Sports.
"Goals always help strikers but he (Rooney) has got a great appetite to play and... to work and fight and gets his rewards eventually.
Villa briefly threatened when new signing Darren Bent scored after 58 minutes only for United defender Nemanja Vidic to finish superbly after Rooney set him up five minutes later.
Winger Ashley Young hit the bar with a long-range curler for the visitors but United always looked to have another gear in reserve.
In contrast Arsenal had to dig deep after Louis Saha put Everton ahead after 24 minutes.
The Merseysiders, who led 2-1 until the last minute in the same fixture last season, defended well until Andriy Arshavin lashed in the equaliser after 70 minutes.
Poor Everton marking allowed Laurent Koscielny to head Arsenal's second from a corner five minutes later.
"We were not as crisp today but you could see how strong the belief is in this team," Arsenal manager Arsene Wenger told the BBC. "We had to rely on our exceptional spirit and attitude and managed to turn this game around."
Sunderland, who beat Chelsea 3-0 at Stamford Bridge in November, went ahead after four minutes through