City's win - boosted further by Chelsea's defeat to Aston Villa - saw them bounce back from FA Cup and Champions League exits to Wigan and Barcelona in the last week despite playing for 80 minutes with 10 men after captain Vincent Kompany was sent off.
Coach Manuel Pellegrini said: "We needed to win and playing with one player less for 80 minutes was very difficult."
City won with goals from David Silva after 14 minutes and Edin Dzeko in the 90th.
Chelsea have six points more than City, but have played three more matches. Liverpool and Arsenal, in third and fourth with 59 points, visit seventh-placed Manchester United and Tottenham, who are fifth, respectively today.
West Ham stayed on the fringes of the relegation scrap after losing 3-1 at Stoke City while Fulham remained bottom, but won for the first time since New Year's Day and for the first time since German Felix Magath became coach.
They beat Newcastle 1-0 at Craven Cottage with a second-half winner from Ashkan Dejagah.
Crystal Palace slipped to 17th despite drawing 0-0 at Sunderland. And West Brom, without a win in their first seven matches under Pepe Mel, ended that sequence with a 2-1 win at Swansea City.
Cardiff City lost 2-1 at Everton where Seamus Coleman hit the winner with almost the last kick of the game.
Meanwhile, two late goals could not save Norwich from a 4-2 defeat at Southampton.