City, who confirmed this week that they have acquired a Major League Soccer franchise, fell behind to goals from Demba Ba, Cesar Azpilicueta and Oscar.
But Javi Garcia began the fightback, Edin Dzeko struck twice and Micah Richards grabbed a dramatic late winner in front of a crowd of 48,263.
Whilst the match did not quite have the intensity of a Premier League match, it was far from half-hearted.
City made all the early running and Chelsea's opener was against the run of play, Joe Hart misjudging Juan Mata's cross and allowing Ba to nod home.
Petr Cech kept out a long-range Yaya Toure effort and Carlos Tevez went close with an overhead kick.
But on the stroke of half-time Karim Rekik was adjudged to have bundled over Mata and Azpilicueta converted from the spot.
Just after half-time City gave the ball away in front of their own area and Oscar danced through to take the ball round replacement goalkeeper Richard Wright.
Then came City's magnificent fightback. Garcia turned in from a corner moments after substitute goalkeeper Jamal Blackman came on and Dzeko then finished expertly from a beautifully weighted James Milner pass.
Blackman then somehow kept out Milner's close range volley, then did superbly to keep out another Dzeko attempt.
But the equaliser came on 85 when Tevez slipped in Dzeko and Richards turned in Garcia's nod-down.
The two teams will meet again at Yankee Stadium in New York on Saturday.