City, who climbed to second in the table, had captain Vincent Kompany sent off after 10 minutes for hauling down striker Nikica Jelavic on the edge of his own box.
They went on to win with goals from David Silva and Edin Dzeko.
League leaders Chelsea, who have six points more than City but have played two more matches, were playing Aston Villa at 1730 GMT.
Liverpool and Arsenal, who are third and fourth, play at Manchester United and Tottenham Hotspur respectively on Sunday.
At the other end Fulham stayed bottom but won for the first time since New Year's Day and for the first time since Felix Magath became coach.
They beat Newcastle United, without suspended manager Alan Pardew in the stadium, 1-0 at Craven Cottage with a second-half winner from Ashkan Dejagah.
Three of the four relegation-threatened teams immediately above them avoided defeat.
Crystal Palace, slipped a place to 17th despite drawing 0-0 at Sunderland, who moved up a spot to 18th.
West Bromwich Albion, without a win in their first seven matches under Spanish coach Pepe Mel, finally ended that sequence with a 2-1 come-from-behind win at Swansea City with goals from Stephane Sessegnon and Youssouf Mulumbu five minutes from time. They went up one place to 16th.
Cardiff City lost 2-1 at Everton, where Seamus Coleman scored the winner with almost the last kick of the game, and slipped back to 19th.
In the other two games Stoke City beat West Ham United 3-1 while two late goals could not save 15th placed Norwich City from a 4-2 defeat at Southampton.
(Reporting by Mike Collett; editing by Justin Palmer and Pritha Sarkar)
