The Gunners were lucky not to lose by a heavier margin than 3-0 at Eastlands where they looked a team in disarray as they crashed to a fifth Premier League defeat of the season.
Arsenal were without nine senior players including William Gallas, stripped of the captaincy after an outburst earlier in the week, the suspended Cesc Fabregas and injured Emmanuel Adebayor and Theo Walcott.
While it was an afternoon to forget for Arsenal, it was one to remember for City who produced one of their best displays of the campaign.
After winning only once in their previous eight league games to slip to one point from the relegation places, this was a morale-boosting victory which eased the pressure on manager Mark Hughes.
It was a measure of how disappointing the opening was that the biggest cheer came when Hughes sent substitute Elano to the touchline to warm up midway through the first half.
City had only a couple of decent chances, Robinho's angled shot bringing keeper Manuel Almunia to his knees while Benjani slid in to make contact with a Darius Vassell cross only to put his effort narrowly wide.
Arsenal, for all their slick passing moves, did not create a chance until the 35th minute when Samir Nasri's free-kick was fumbled by keeper Joe Hart while Alexandre Song fired the rebound wide.
Then, in first-half stoppage time came the breakthrough for City, as Stephen Ireland broke through the visiting defence after Mikael Silvestre and Gael Clichy had collided to enable the midfield player to score with ease.
Arsenal made a lively start to the second half, but it was City who doubled their advantage in the 56th minute when Shaun Wright-Phillips played an inch-perfect pass to release Robinho who lobbed Almunia from the edge of the penalty area for his ninth goal of the season.
Robinho was denied a second goal by the referee's assistant who flagged for offside after he had tapped in the ball from almost on the goal-line after Almunia had fumbled Ireland's shot.
Robinho had two further great chances to complete a second hat-trick for City but he was denied by Almunia and then a goal-line clearance from Johan Djourou.
Arsenal's misery was completed when they conceded a third goal in stoppage time. After Djourou has tripped substitute Daniel Sturridge, the young City striker got up to score from the spot himself.