With the champions facing a tough trip to London rivals Arsenal on Sunday, United needed to keep up the pressure with a win and a goal in each half by strikers Ruud van Nistelrooy and Wayne Rooney ensured they did so.
Chelsea have 43 points from 16 games with United on 37 points from 17 matches. Third-placed Liverpool, on 31 points, are in Japan taking part in the Club World Championship.
Elsewhere on Saturday fifth-placed Bolton Wanderers crushed Everton 4-0 at Goodison Park and Portsmouth marked manager Harry Redknapp's first home match back in charge with a 1-0 win over fellow strugglers West Bromwich Albion.
Senegalese forward Henri Camara hit a hat-trick to give Wigan Athletic a 3-0 home win over Charlton Athletic and England striker Michael Owen also scored three in Newcastle United's 4-2 win at West Ham United. Fulham beat Blackburn Rovers 2-1.
Manchester City thrashed Birmingham City 4-1 in a late game in the northwest that will turn up the pressure on the visitors' manager Steve Bruce.
United quickly took control at Villa Park and almost opened the scoring when South Korean midfielder Park Ji-sung fired against the post.
Two minutes later Van Nistelrooy put them in front when he collected a Darren Fletcher pass, shrugged off his marker and lifted the ball over Villa goalkeeper Thomas Sorensen.
Rooney added a second with an emphatic low finish from Park's pass five minutes into the second half.
Villa's Milan Baros struck the bar but United finished the match in exhibition mode with Portuguese winger Cristiano Ronaldo producing some party tricks to provide a cross that Van Nistelrooy could not quite direct into the net.
United have now won all 21 of the matches in which England striker Rooney has scored for them and the victory was a further morale-boost to Alex Ferguson's side after their costly Champions League exit.
On Wednesday they thrashed Wigan Athletic 4-0.
"We're nine points behind Chelsea if they win their game tomorrow," Ferguson told Sky Sports TV. "It's a long way, but what we can do is to make sure we win our games and if we do and if Chelsea slip up hopefully we will be the team nearest to them."
Everton's mini-revival has ground to a halt, with Greek striker Stelios Giannakopoulos's double strike the highlight of Bolton's emphatic victory at Goodison.
His first was a deft finish after 75 minutes and his second a long-range piledriver as Bolton joined fourth-placed Tottenham Hotspur on 30 points.
CAMARA TRICK
Portsmouth earned their first home win of the season thanks to Bulgarian striker Svetoslav Todorov. His 56th-minute winner assured Redknapp of a perfect reception in his first match back at Fratton Park since his controversial switch to their south-coast rivals Southampton.
The win pulled third-from-bottom Portsmouth to within three points of fourth-from-bottom West Brom.
"Great result, we needed that badly," Redknapp told Sky Sports. "We worked our socks off... you can't ask for any more."
Camara doubled his tally for the season with a sparkling treble against Charlton to end Wigan's poor recent run and lift them up to sixth place.
Newcastle's match at West Ham was subject to a delayed kickoff due to a traffic accident but it proved to be worth the wait for the visitors.
Three cool finishes by Owen and a spectacular strike by former England captain Alan Shearer left West Ham in tatters at Upton Park and eased further the pressure on Newcastle manager Graeme Souness.
Portuguese forward Luis Boa Morte netted what proved to the winner in Fulham's much-needed win over Blackburn.
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