Arsenal continued to bang in the goals with a 3-1 home victory over Birmingham City while Tottenham Hotspur survived a 60th-minute red card for Jermain Defoe to secure a 2-1 win at Portsmouth.
Champions United lead the way with 22 points from nine games. Chelsea are second on 21, Spurs have 19 and Arsenal have a game in hand on 18 points.
United needed a last-minute own goal to salvage a 2-2 home draw with Sunderland in their last league game and it was another own goal that put them ahead on Saturday as Zat Knight's attempted clearance flew in after five minutes.
The home team looked too good for their Lancashire rivals in the first half and the second goal came after 33 minutes when Antonio Valencia fired his first for the club since his close-season move from Wigan.
Some loose defending allowed Matt Taylor to pull one back for Bolton after 75 minutes and set up a nervous finale for the United fans.
"When Bolton scored it was backs to the wall stuff and there was a bit of panic," United manager Alex Ferguson told Sky Sports.
"They are the sort of team who can take points off anyone, they are difficult opponents so we are quite happy to get the result."
Liverpool's hopes of a first title in 20 years already look slim after a fourth defeat in nine league games, though they were furious Sunderland's controversial goal stood.
The key moment came after five minutes when Darren Bent's shot cannoned in off a loose beach ball which had "Liverpool" written on it.
The visitors, without the injured Steven Gerrard and Fernando Torres, complained but Bent was happy to claim his sixth goal in five games.
Former FIFA referee Graham Poll told the BBC that according to the laws, play should have been stopped and a drop ball given.
"If that's the case then we've got away with one," Sunderland manager Steve Bruce told the BBC.
Bent said: "The beach ball was sitting there in their six-yard box so if they leave it there they pay the penalty."
Portsmouth remained rooted to the bottom on three points after Spurs, who raided the south coast club for manager Harry Redknapp, his assistant coaches and several leading players last season, won with goals by Ledley King and Defoe.
Kevin-Prince Boateng pulled one back but even after former Pompey striker Defoe was sent off, Spurs held on.
Pompey also had Michael Brown sent off in added time while Redknapp, who led Portsmouth to FA Cup glory 18 months ago, remained seated in the dugout throughout the match.
Arsenal looked to be cruising after two goals in three minutes by Robin van Persie and Abou Diaby in the first half but Lee Bowyer pulled one back for Birmingham.
As the visitors poured forward looking for an equaliser Arsenal broke in typical style, Andrei Arshavin getting the third with five minutes to go to take their tally of league goals to 27.
Chelsea's win at Villa Park last season was their fi
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