Wayne Rooney’s penalty and an own goal by Abou Diaby gave Manchester United a 2-1 victory over Arsenal in the Premier League and Chelsea and Tottenham both won to stay neck-and-neck at the top of the standings.

Arsenal went ahead through a 20-metre strike by Andrei Arshavin in the 40th minute at Old Trafford in a game marred by too many fouls and needless yellow cards. But Rooney equalised in the 59th from the penalty spot after he had been brought down by Arsenal goalkeeper Manuel Almunia and Diaby headed a free kick from Ryan Giggs into his own net five minutes later.

A minute before Arshavin’s goal, Arsenal should have had a penalty when the Russian was brought down by Darren Fletcher and Robin van Persie hit the United crossbar with a bending free kick. But United should have added further goals near the end when Dimitar Berbatov and Nani missed simple chances.

Van Persie had the ball in the net in the fifth minute of injury time but it was ruled out for offside against William Gallas and the game ended with farcical scenes when Arsenal manager Arsene Wenger, furious at some of the referee’s decision, was ordered off the bench and sent to the stands.

Chelsea scored three goals in seven minutes to secure a 3-0 home victory over Burnley to take Carlo Ancelotti’s team to the top on goal difference. Counting last season’s last five matches, Chelsea have now won nine in a row in the league.

“I am very happy not just because of the result but because of the play of the team,” said Ancelotti, who is in his first season in English football after moving from AC Milan. “I am very proud to train this team because they have a lot of quality.”

After Martin Paterson had missed a great chance for Burnley at Stamford Bridge, firing wide of the post while unmarked, Nicolas Anelka gave Chelsea the lead in first half injury time when he turned home a cross from strike partner Didier Drogba.

Michael Ballack headed home a cross from Frank Lampard in the 48th minute and Ashley Cole swapped passes with Lampard and drove a shot into the roof of the net in the 52nd.

“It’s my third season (at Chelsea) now and for me we are getting more and more like a family and the spirit is better than I have ever seen here,” said Cole, whose team finished third behind Manchester United and Liverpool last season. “We are hungry to win, we didn’t like losing last season and hopefully this season can be our year.”

After hitting the bar and missing two more chances, Peter Crouch headed Tottenham in front from a free kick by Tom Huddlestone in the 72nd minute against Birmingham.

Three minutes later Lee Bowyer equalised but Lennon fired home Roman Pavlyuchenko’s cross for the winner in injury time.

Steven Gerrard scored Liverpool’s 83rd minute winner after last season’s runner up had twice trailed at Bolton and appeared to be headed for a third defeat in four games.

Kevin Davies fired Bolton ahead and, although Glen Johnson equalised, Tamir Cohen made it 2-1 in the 47th minute. Bolton had Sean Davies sent off for two yellow cards in the 54th and, two minutes later, Fernando Torres netted his third goal in three games.

“There was a lot of soul-searching throughout the week and the manager told us he wanted to see character, determination and intensity,” said Gerrard, who fired home a 17-metre shot for the winner. “I think he got the three things he asked for.”

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