Chelsea have spent more than 60 million pounds over the close season while City's only major deal has been signing of Everton's Jack Rodwell which was announced earlier on Sunday, pending a medical.
However, goals from Yaya Toure, Carlos Tevez and Samir Nasri in a 12-minute second half spell showed that the Premier League champions may have enough firepower as it is.
With Wembley in use for the Olympic Games, Birmingham's Villa Park hosted the traditional curtain-raiser to the English season a week before the start of the Premier League.
City were helped by the first-half dismissal of Chelsea's Branislav Ivanovic for a reckless challenge on Aleksandar Kolarov.
City captain Vincent Kompany told ITV he would not be drawn on Ivanovic's red card but thought his side was well on top before the dismissal.
"To be honest I was little bit far from the action so I didn't see, all I can say is even before the red card I thought we had more possession," he said.
"Probably the two goals they scored were the only two chances they had."
"I don't know what we proved today, I just think it was a great day for the club again. It doesn't matter whatever the trophy is, we'll celebrate. We are so happy."
