LONDON, England (AP) — Manchester United’s seven-point lead over neighbour Manchester City stayed intact after the title-chasing rivals downed two of the Premier League’s fallen giants in contrasting ways yesterday.

While United ended up scraping to a nervy 2-1 win at home to Liverpool, City sauntered to a 2-0 victory at Arsenal after playing against 10 men for most of the match.

Laurent Koscielny’s ninth-minute red card for wrestling Edin Dzeko to the ground inside the area proved decisive, with Dzeko missing the resulting penalty, but later adding to the superb opener by James Milner. The only negative for City after their first league win at Arsenal in 38 years was the red card awarded to Vincent Kompany for a two-footed tackle, which will deprive the team of its captain for three games.

Robin van Persie set United on the way to victory over their greatest rival at Old Trafford with his league-high 17th goal of the campaign. Nemanja Vidic unwittingly made it 2-0, but United had to resort to some desperate defending to preserve the lead after substitute Daniel Sturridge’s goal on his league debut for Liverpool.

“It was a big game, everyone felt that during the week, and this is a great result,” said Van Persie, whose arrival from Arsenal in August is proving to be a big factor in the title battle.

Many pundits were dubbing this weekend a pivotal moment in the title race but the status quo remains with 16 matches still to play. Chelsea, a 4-0 winner at Stoke on Saturday, can keep their slim hopes of catching the Manchester clubs alive by beating Southampton on Wednesday in their game in hand to reduce the gap to United to 11 points.

Playing in the day’s early kickoff, United had piled the pressure on City by holding off a valiant fightback from Liverpool after getting themselves into a position to coast home at Old Trafford.

“The name of the game is winning,” United manager Alex Ferguson said. “There are moments where you have to defend. Today was one of them.”

Van Persie’s well-taken finish — his ninth goal in his last nine games — in the 19th minute came from one of a host of first-half chances created against a slovenly Liverpool team that gave the ball away with alarming regularity early on.

When Vidic made it 2-0 in the 54th by glancing in Patrice Evra’s downward header, United relaxed and Liverpool started to threaten. Sturridge, who transformed Liverpool following his arrival at the start of the second half, reduced the deficit from close range within three minutes, but missed the best of the chances to equalise late on.

“I am very proud of the fight of the team in the second half having gone 2-0 down,” said Liverpool manager Brendan Rodgers, whose side stayed in eighth place. “Teams who come here often crumble, but I thought by the end we deserved something to be honest.”

Arsenal and Liverpool used to be regular challengers for the title but their main target nowadays is qualification for the Champions League.

Even that might be beyond Arsenal this season, with the loss to City leaving Arsene Wenger’s side six points adrift of fourth-place Tottenham in sixth.

From the moment Koscielny was dismissed for hauling Dzeko to the ground, the hosts were always up against it.

“We started too timidly with not enough authority … and we paid for it,” Wenger said. “Playing 80 minutes with 10 men against 11 is difficult.”

City ensured there would be no coming back for Arsenal by scoring twice in a 12-minute span midway through the first half. Milner drove in the 21st-minute opening goal from Carlos Tevez’s cute pass and then supplied the cross that Dzeko ended up tapping in after Tevez’s flick-on was saved.

“Them going down to 10 men helped (but) before the sending-off, we looked the most dangerous side anyway,” Milner said. “It was important we did not give them a sniff.”

With City having come from eight points behind with six games left to win the title last season, the current seven-point gap doesn’t concern manager Roberto Mancini.

“United is a strong team — at this moment, they are playing very well,” he said, “but this season is long and it’s important we are still there.”

Mancini said City will be appealing against Kompany’s sending-off, given in the 75th minute when he left the ground and lunged studs-first at Jack Wilshere.

“It’s absolutely not a red card. He anticipated the opponent,” Mancini said. “He (Kompany) is disappointed. He said, ‘I did nothing.”‘