Goals from England midfielder Paul Scholes and Dutch striker Ruud van Nistelrooy earned champions United their victory at The Reebok, while a 75th-minute equaliser from Everton's Canadian forward Tomasz Radzinski denied Arsenal all three points at Goodison Park.
Chelsea, who were beaten by Frenchman Bruno Cheyrou's first-half goal, are now seven points off the title pace having lost three and drawn one of their last six league games.
The results were all good news for Alex Ferguson's United, who head the table with 49 points, ahead of second-placed Arsenal on 46. Chelsea stay third on 42.
Charlton Athletic are fourth on 31 points after Paolo Di Canio earned them a 1-1 draw with Manchester City but Liverpool and Newcastle United, who beat Leeds United 1-0 with a goal by skipper Alan Shearer, have now both closed to within two points on 29.
Manchester United confirmed their status as title favourites as Scholes and Van Nistelrooy, scoring his 14th league goal of the season, established a two-goal lead at the break.
Bolton finished strongly and French playmaker Youri Djorkaeff pulled one back in the 89th minute, but as their boss Sam Allardyce admitted: "It was down to our poor defending in the end...and that against Manchester United is criminal."
GOOD NIGHT
A buoyant Ferguson told Sky Sports: "Collectively we are playing some really good football, not many teams will win at Bolton.
"It's been a good night for us with the bonus of other teams dropping points."
Arsenal, whose 30-match unbeaten run was ended by Everton last season, lacked their usual sparkle at Goodison Park despite Nigerian forward Nwankwo Kanu giving them a first-half lead.
Their consolation, after Radzinski's late equaliser, was to maintain their unbeaten start to this season, now 20 matches.
The real surprise, though, came at Stamford Bridge where Liverpool had lost their last eight games against Chelsea.
The visitors were missing injured skipper Steven Gerrard and had to replace injured keeper Jerzy Dudek in the second half, while England striker Michael Owen was on the bench.
But Liverpool, whose defeat in this fixture last season gave Chelsea a Champions League qualifying place at their expense, took their revenge with a determined performance.
"We know this is not our best moment," said Chelsea coach Claudio Ranieri. "We are trying to do everything well but it's just not happening."
Victory for Liverpool was a big relief after criticism of their recent form and a hint earlier this week from chairman David Moores that he might stand down at the end of the season if the team's results did not improve.
"We've had a difficult week and it was an ideal opportunity for the players to respond and to show the critics are wrong," manager Gerard Houllier said.
"It was a great game to show not only the talent but also the togetherness and determination of the team.
"We're not happy with the results this season, but we also know why and I'm sure we'll get better and better in 2004."
