Edin Dzeko scored twice — his first coming inside 43 seconds — and Yaya Toure added a late third at Old Trafford for City, which trimmed its deficit to leader Chelsea to three points and still has two games in hand.
United lost for the sixth time in the league this season — more than in the last three campaigns combined — in what is proving a woeful defence of its title under David Moyes. Five points behind sixth-place Tottenham with seven games left, even finishing in the Europa League positions may be beyond beleaguered United.
"I thought it would be a tough year for us, no doubt about that," said Moyes, whose team is 18 points behind Chelsea, "but I hoped it would be much more competitive and closer to the top of the league than we are at the present time."
Arsenal conceded an own goal by Mathieu Flamini in the 90th minute to drop more points in the title race after a 6-0 thrashing by Chelsea on Saturday.
Arsene Wenger's side is six points behind the leaders in fourth place and is now looking over its shoulder at Everton, which jumped to fifth with a 3-0 win at Newcastle in the night's other match.
Everton is six points behind Arsenal having played a game less.
"It's difficult to swallow because the team gave absolutely everything, their spirit was great," said Wenger, whose side fell behind before Lukas Podolski and Olivier Giroud scored goals in a 70-second span. "You wonder how we could draw a game like that — they had nothing and in the end it was 2-2."
Liverpool can climb back up to second place, and within a point of Chelsea, by beating Sunderland on Wednesday.
City may have installed itself as title favourite now, though, by dismantling it neighbour to send out another a statement of intent and secure a third straight league win at Old Trafford.
Just like 10 days ago when United was humiliated by Liverpool on its own ground, the deficiencies of Moyes' side were laid bare against its other biggest domestic foe.
It took less than a minute for Dzeko to open the scoring, bundling home a rebound after Samir Nasri's shot struck a post. And the same combination delivered the second goal, Nasri's outswinging corner volleyed home sweetly by the Bosnia striker.
City had to wait until seconds remaining of normal time for Toure to add a third — and it could have been a lot worse on another chastening night for Moyes.
"We can't lose six home games in a season," United striker Wayne Rooney said, "and we have to put that right, and make this a place which teams fear again."
When asked if the title was City's to lose, manager Manuel Pellegrini said: "I don't think so. The title race continues, we continue fighting with all the other three, Arsenal, Chelsea, Liverpool."
To many, however, Arsenal's chance has passed.
The Gunners trailed after Wilfried Bony's goal in the 11th but substitute Lukas Podolski equalized in the 73rd and then set up Giroud barely a minute later.
Arsenal was within sight of closing the gap to Chelsea to four points, only for Per Mertesacker to slide in front of Leon Britton as he attempted to clear, with the ball bouncing off goalkeeper Wojciech Szczesny onto Flamini and into the net.
"This result tonight hurts us a lot," Wenger said.
Arsenal could virtually be knocked out of contention if it fails to beat City on Sunday.
Ross Barkley sparked Everton's win by embarking on a dribble from inside his own half, powering through Newcastle's defence and blasting home a fierce shot in the 22nd minute.
Romelu Lukaku and Leon Osman scored the other goals in the second half.Suggest a correction