The reigning champions, bidding for an 18th English title, chalked up a 10th consecutive clean sheet in the league on a day of late goals and red cards in the top flight.
Chelsea breathed a huge sigh of relief as England midfielder Frank Lampard struck four minutes into stoppage time to earn a 2-1 victory over Stoke City at Stamford Bridge after Brazilian Juliano Belletti had equalised for the Blues after 88 minutes.
Lampard wore the captain's armband after defender John Terry suffered a back spasm in the pre-match warm-up.
Luiz Felipe Scolari's side, who earlier discovered that midfielder Joe Cole will miss the rest of the season with a serious knee injury, stayed third, just ahead of Aston Villa who came from a goal down to beat Sunderland 2-1 away despite having striker Ashley Young sent off.
United have 47 points from 21 matches, one ahead of Liverpool who can reclaim top spot with victory over Everton on Monday. Chelsea have 45 points from 22 matches with Villa on 44.
Fifth-placed Arsenal have 41 points after goals from Samir Nasri and Nicklas Bendtner in the final 10 minutes earned a 3-1 victory at Hull City.
United manager Alex Ferguson said it was a good to top the table, even if only for 48 hours.
"The way their keeper was performing it looked like it wouldn't happen," United manager Alex Ferguson told Sky Sports. "We left it very late.
"It's not decisive but it's always nice to be in the lead, it's the best place to be although of course Liverpool go to Everton on Monday.
"We can reflect on a very, very good period for us," added Ferguson whose side have kept pace in the title race despite a pre-Christmas trip to Japan to claim FIFA's World Club title.
Manchester City put aside the hype surrounding their world-record bid for AC Milan's Kaka to beat Wigan Athletic 1-0 at Eastlands despite ending the match with 10 men after defender Richard Dunne was sent off.
While the battle for the title looks to be the most open for many years, the dogfight at the bottom is equally fascinating.
West Bromwich Albion moved off the bottom with a 3-0 thrashing of Middlesbrough and Blackburn Rovers climbed out of the relegation zone with a 3-0 defeat of Newcastle United, for whom midfielder Nicky Butt was dismissed.
SPURS SLIDE
Tottenham Hotspur are now bottom with 20 points, although they can move out of the drop zone with victory at home to Portsmouth on Sunday.
For the second time in a week United ground out a precious three points, having beaten Wigan Athletic 1-0 on Wednesday.
Despite the attacking tolls at their disposal, United's hot streak has been based on a watertight defence and Saturday's clean sheet against Bolton equalled Chelsea's Premier League record despite the absence of Rio Ferdinand and Patrice Evra.
