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Champions United edged out Liverpool at Anfield to briefly top the table, but Arsenal restored their one-point advantage with a similar victory over Chelsea.

 A rare mistake from Petr Cech handed Arsenal the winning goal on the stroke of half-time as he failed to claim a corner, leaving former Chelsea man William Gallas to head into an empty net.

 John Terry was forced off with a suspected metatarsal injury but Chelsea chased the equaliser in the second half and Shaun Wright- Phillips should have scored only to drag his shot well wide from four yards.

 At the other end, substitute Robin van Persie had a goal ruled out for offside, while the Dutchman also went close on several other occasions, although Manuel Almunia had to tip over a shot from Andriy Shevchenko.

 Chelsea are now six points behind Arsenal, with Liverpool fifth, 10 points behind, though they have played a game less.

 "Today I was a little bit lucky as Petr is usually a good, good goalkeeper," Gallas said.

 "But it is more important to win and I feel the boys did need to win today against a good team. Everybody knows Chelsea are very strong.

 "We know we now have six points (advantage over Chelsea) and that is very important."

   Arsenal manager Arsene Wenger said the title race was still wide open.

 "There is nothing decisive. Liverpool have lost many points at home, they need to come back but are still in contention and Chelsea today showed they can still fight for the championship.

 "But at the moment the most consistent are Manchester United and Arsenal."

   At Anfield, Liverpool dominated the match in terms of possession but United snatched victory when Carlos Tevez side-footed home three minutes before half-time.

 "It's a marvellous day for us," United manager Sir Alex Ferguson said.

 "It was a good team performance and a great result. I said before the game that I feel the games between the top sides are going to be important this season. That's an important win for us.

 "It's going to be a long struggle and a fight until the end of the season. But I've always said (if) around December, if we can be top or thereabouts on New Year's Day then we have an outstanding chance of retaining the title."

   Liverpool had the better of the first half and United needed some last-ditch defending to stop Rafael Benitez's side from taking the lead.

 Two mistakes by Edwin van der Sar put United in trouble but Harry Kewell's shot was cleared off the line by Anderson and Patrice Evra then covered well to prevent a header from Fernando Torres crossing the line.

 The two sides looked to be heading for half-time with the scores still goalless when United took the lead against the run of play.

 A corner from Ryan Giggs was pulled back for Wayne Rooney and his scuffed shot went through the legs of Jamie Carragher to Carlos Tevez, who lifted the ball into the roof of the net.

 Liverpool brought Ryan Babel and Peter Crouch midway through the second half and Babel fired a superb shot just wide.

 Rooney should have made it 2-0 after a great ball from Cristiano Ronaldo, but the England striker side-footed wide.

 Peter Crouch also shot wide late on and Steven Gerrard lifted a free-kick just over the bar in injury time as United held on for victory.

 Liverpool manager Benitez, whose side are now nine points behind United, albeit with a game in hand, said it was too soon to say they are out of the title race.

 "There is still a long way to go," he said.

 "It will be harder after this game but we have to keep going and think about our next game."

   Benitez said his team had been beaten by a sucker-punch of a goal.

 "In the first half we create two good chances but we didn't take them, and they created one chance and scored," he said. "We made a mistake for their goal but you need to take your chances. If you do that you will be in a very good position."

By Ben James, dpa