James Milner and Kieran Gibbs (AP)

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London - English Premier League champions Manchester City remained seven points adrift of leaders Manchester United after a 2-0 win away to Arsenal on Sunday, with both teams finishing a man down in an eventful match.

First-half goals from James Milner and Edin Dzeko put City in a commanding position against Arsenal, already reduced to 10 men after Laurent Koscielny was sent off in the 10th minute for bringing down Dzeko inside the box.

Although Dzeko's penalty following Koscielny's red card was turned onto the post by Wojciech Szczesny, with the Arsenal goalkeeper gathering the rebound, it was not long before Milner and Dzeko himself made the man advantage count.

VIDEO: Arsenal v Manchester City highlights

"I don't know about the sending off, but it was a penalty 100%. I told myself after missing the penalty I had to score," said Dzeko.

The visitors too were a man down at the Emirates Stadium when, 15 minutes from time, City captain Vincent Kompany was dismissed by referee Mike Dean for a challenge on Jack Wilshere despite appearing to win the ball first.

Arsenal, without a major trophy since 2005, remained sixth in the table as City enjoyed their first league win away to the Gunners since 1975.

Second-placed City, who failed to sell their allocation of seats for the match after some fans complained about tickets priced at £62 each, were briefly 10 points adrift of United after their cross-town rivals beat Liverpool 2-1 at Old Trafford earlier on Sunday.

Goals from Robin van Persie and Nemanja Vidic gave United a 2-0 lead before Liverpool substitute Daniel Sturridge pulled one back for the visitors.

"It obviously doesn't matter when you play Liverpool, it is a big game and I hope it's an important result," United manager Alex Ferguson told the BBC.

"We were fantastic until their goal, which inspired them. They made a fist of it in last half hour and it made it an engrossing game. When you play Liverpool you have to be at your best form to win and we were."

Van Persie gave United a 19th minute lead when he swept in Patrice Evra's cross from eight yards out.

It was the Dutch striker's 17th Premier League goal this term, and 21st in all competitions, since he arrived at Old Trafford in a £24m pre-season move from Arsenal.

United made it 2-0 nine minutes after half-time when full-back Evra's header from van Persie's free-kick deflected in off centre-half Vidic.

But three minutes later Sturridge, on at the start of the second half for Lucas Leiva, marked his Premier League debut for Liverpool with a goal when he followed up the rebound after David de Gea saved skipper Steven Gerrard's shot from outside the box.

It was Sturridge's second goal in as many games for Liverpool following his move from European champions champions Chelsea after he was on target in the 2-1 FA Cup win over Mansfield last weekend.

However, Sturridge failed to make the most of two more chances and United, who've won a record 19 English titles compared to Liverpool's 18, held on for a hard-fought victory.

Liverpool remained eighth in the table, albeit now 24 points adrift of United, and manager Brendan Rodgers praised his team's resilience.

"In the second half, after we conceded the goal, we could have given up the fight but that is the nature of the group," Rodgers said. "In the end, I thought we maybe deserved something from the game.

"He (Daniel Sturridge) was terrific when he came on and we were much better in the second half."