Fernando Torres put Chelsea ahead in the 40th minute, but the game turned after his teammate Branislav Ivanovic was sent off just moments later. Three goals in 12 minutes from Yaya Toure, Carlos Tevez and Samir Nasri put City firmly in control before Ryan Bertrand scored a late second for Chelsea.
For Premier League winner City, it was a first success since 1972 in the annual curtain raiser between the English champions and the FA Cup holders.
"It was a good performance," City coach Roberto Mancini said of his side's display, though he acknowledged the advantage of having an extra man.
"It had an impact on the game. It is impossible to say 'no' because 11 versus 11 is different. But we played better than Chelsea, played better football."
Chelsea coach Roberto Di Matteo had no doubt that the red card issued by referee Kevin Friend was the turning point.
"It changed the game in favour of Manchester City," he said." We competed very well and at that point were in the lead. It was difficult in the second half against 10 men."
Ramires created Chelsea's opener, nipping past Pablo Zabaleta before surging into the box and flicking an astute pass past Eden Hazard to Torres on his right. The Spain striker showed signs last season of starting to find his old form and his contribution on Sunday was clinical, beating the advancing Costel Pantilimon with the predatory instinct of old.
Pantilimon had been given a rare start due to Joe Hart's back injury.
Two minutes later, Chelsea's positive start was compromised by Ivanovic being shown a straight red card. Forced to challenge for a stray pass by John Terry, the Serbian slid straight into countryman Aleksandar Kolarov, studs raised. Though not two-footed, it was dangerous.
Ivanovic will now miss next week's trip to Wigan, plus home encounters with Reading and Newcastle.
Tevez, Nasri and skipper Vincent Kompany had all gone close for City, but it was Toure who once again made the vital breakthrough.
Seizing on Terry's poor clearance, the midfielder drilled a fierce shot straight back through a crowd of bodies, giving Petr Cech no chance.
Now City had the momentum, and the champions made the extra man tell.
Six minutes later, neither David Luiz nor Terry were able to check Tevez's darting run along the edge of the penalty area. From a central position, Tevez hammered a superb shot into the top corner to put City ahead.
Six minutes after that, Kolarov streaked past makeshift right-back Ramires and curled a cross to the near post which Nasri touched home.
If Ramires had not managed to steer James Milner's cross over the bar, an unmarked Tevez would have had a tap-in as a rampant City poured forward.
Yet it was Chelsea who scored 10 minutes from time, through substitute Bertrand, who promptly became involved in a spat with Pantilimon as he tried to wrestle the ball away to restart the game.
City came closer to grabbing a fourth than Chelsea an equaliser though, when Sergio Aguero somehow managed to turn James Milner's cross wide in the final minute when it seemed easier to score.
However, City had already done enough in a game that was moved to to Villa Park from Wembley Stadium because of the London Olympics.