Arsenal moved into second in the Premier League after a 3-0 win over 10-man Manchester City on Sunday, while Manchester United beat Stoke City 2-1, dpa reported.
Liverpool won their second game of the season, beating Blackburn Rovers 2-1.
City could have closed to within two points of leaders Chelsea, but they were always on the back foot after Dedryck Boyata was sent off in the fifth minute.
In a pulsating game, Samir Nasri put Arsenal ahead and Cesc Fabregas missed a penalty before second-half goals from Alex Song and Nicklas Bendtner made the game safe.
"I think we played some outstanding football and it's difficult to stop a side when they play at that tempo," said Fabregas. "It's very difficult what to know what will happen, but it's a good victory against a good team."
Arsenal, United and City all have 17 points, five behind Chelsea, while Liverpool remain in the relegation zone.
Arsenal keeper Lukasz Fabianski was called into action in the first minute, making a fine save low to his right as David Silva got a touch on a Carlos Tevez cross.
Micah Richards then got away on the same flank, but just as City seemed to be taking control and exposing Gael Clichy on the Arsenal left, Boyata chopped down Marouane Chamakh as he made a burst towards the box and was rightly sent off with only five minutes played.
"I think it was the worst moment to go down to 10 men but I am very proud of my players," said City manager Roberto Mancini.
"They played well and stayed in the game until the second goal.
"I think after today we must say we are one of the best teams in the Premier League. If it was 11 against 11 we would have won this game."
City remained positive, but it was Arsenal who took the lead after 20 minutes, Samir Nasri playing a one-two with Andrei Arshavin before slamming his finish past Joe Hart.
Richards bent a shot just wide after another surge down the right, as City looked more threatening side.
But six minutes before half-time Vincent Kompany tripped Cesc Fabregas in the corner of the box, conceding a penalty.
Fabregas took it, but Hart saved diving to his left. With City threatening and the card count - and thus the chance Arsenal could also be reduced to 10, mounting - thoughts went back to Arsenal missing a penalty while leading at Sunderland and conceding a late equaliser.
City had chances: Silva, cutting in from the right, had a shot form a narrow angle tipped wide by Fabianski, then Emmanuel Adebayor, on for Tevez, who looked injured, headed just over.
But with 66 minutes played, Song added a second, firing into the top corner after Wayne Bridge had half cut-out a Fabregas pass to Chamakh.
And Bendtner added a third form Nasri's pass with two minutes to go.
At Stoke, United threw away a lead for the sixth time this season, but recovered to beat Stoke thanks to two goals from Javier Hernandez.
He put United ahead with a smart back-header, but substitute Tuncay Sanli levelled after 81 minutes.
Hernandez, though, salvaged the win with five minutes remaining, guiding in Patrice Evra's volleyed cross after fine approach work from Dimitar Berbatov.
"It was important we won, drawing so many away games has not been so good," said United right-back Gary Neville.
"When Tuncay's goal went in we thought 'oh no, not again' so the winner was fantastic."
Liverpool remain in the relegation zone despite a 2-1 win over Blackburn. Sotiros Kyrgiakos put them ahead, and Fernando Torres restored their lead after Blackburn had levelled with a Jamie Carragher own-goal.