Middlesbrough fans will be urging manager Steve McClaren to sign Geremi on a permanent basis when the transfer window opens in January.
Geremi, who is on loan from Real Madrid, was a key figure in a worthy win for Middlesbrough.
The talented midfield player scored and contributed to the two other second-half goals.
McClaren said after the game: "I thought it was an excellent game of football and for a neutral observer it must have been great to watch.
"Manchester City contributed to an end to end game. I thought it was a great advert for the Premiership.
"The one thing that surprised me that it was 0-0 at half time. I just told my players to be patient and to wait for the first break." Central defender Ugo Ehiogu set Middlesbrough on the way to success with Croatian international striker Alen Boksic increasing the lead with his first goal of the season.
City hit back with a scrambled goal by Nicolas Anelka, following a defensive lapse by Jonathan Greening, but any hopes the visitors had of pulling the game round where shattered when Shaun Wright-Phillips was sent off for his second bookable offence.
Shaun Goater was ineffective in City's attack and it was no surprise when he was withdrawn from the action.
City manager Kevin Keegan had no complaints with the result or the sending off.
"I don't think we can have any arguments about the result," he said.
"When we got back into the game at 2-1 we had a sniff of a chance. But then we went down to ten men almost immediately.
"From that point Middlesbrough played the best football and we could not get back into the game.
"I'm a big fan of Wright-Phillips but I've no problem with his sending off."