Roberto Mancini’s side knew anything less than a victory at the Emirates Stadium would all but end their title hopes after leaders Manchester United moved 10 points clear with a 2-1 win over Liverpool earlier on Sunday.
But second-placed City showed their determination to hold on to the crown with a first league win on Arsenal turf since October 1975.
The turning point came early on when Arsenal defender Laurent Koscielny was sent off by referee Mike Dean for a professional foul on Edin Dzeko.
Although Dzeko missed the penalty which resulted from that incident, City exploited their numerical superiority in ruthless fashion with goals from James Milner and Dzeko before half-time.
City had captain Vincent Kompany sent off in the closing stages, but it was too late to spark an Arsenal fightback and Mancini’s men, who have won five of their last six league games, will believe they can still overturn United’s seven-point lead.
In contrast, Arsenal’s spluttering attempts to qualify for the Champions League look more unconvincing by the week and Arsene Wenger’s side remain six points behind fourth-placed Tottenham.
City returned a large portion of their 3,000 ticket allocation after fans refused to pay £62 (83 dollars) for seats in the away end, but those who boycotted the fixture missed an historic day for their club.
Police had been called to deal with a suspect package in a car park close to the Emirates before kick-off, but it was Arsenal’s hapless defending that gave more cause for alarm.
City benefited from those frailties in the 10th minute when Koscielny rashly grabbed hold of Dzeko and hauled the Bosnian forward to the turf as the pair contested a high ball in the Arsenal area.
Dean immediately awarded a penalty and sent off Koscielny for his rugby tackle.
It looked like advantage City but Wojciech Szczesny came to Arsenal’s rescue as he deflected Dzeko’s spot-kick onto a post with his legs and then clasped the ball to his body as it rebounded along the goal-line and into his arms.
Dzeko, attempting to make amends for his penalty miss, screwed a shot wildly off target from a tight angle with two City team-mates screaming for a pass.
But City didn’t need to rue Dzeko’s profligacy for long as Arsenal were caught cold by a quick free-kick from Gareth Barry in the 21st minute.
David Silva took Barry’s short pass and moved possession onto Carlos Tevez and, with Arsenal’s defenders responding far too sluggishly, the Argentine had time and space to find Milner 10 yards from goal and the England midfielder lashed a superb strike into the far corner of Szczesny’s goal.
Arsenal’s defence is fragile at the best of times and, with an extra man at their disposal, City were able to pick them apart for their second goal in the 32nd minute.
Pablo Zabaleta brushed Kieran Gibbs aside to steal possession and the City defender released Milner into the space down the left.
With Arsenal completely exposed, Milner whipped over a low cross and Tevez’s shot was pushed out by Szczesny only as far as Dzeko and the Bosnian tapped into the empty net from close-range.
Javi Garcia almost killed off Arsenal just before half-time when his looping header was nodded off the line by Jack Wilshere.
City were content to sit on their lead for much of the second half and Dean gave Arsenal a glimmer of hope in the 75th minute when he ruled that Kompany’s two-footed tackle on Wilshere was worthy of a red card.
But the visitors had to survive only one scare when Joleon Lescott cleared off the line from Theo Walcott.