Everton suffered a surprise 3-2 home defeat by Crystal Palace at Goodison Park to hit their chances of a top-four finish.
Fernandinho got City off to the perfect start with a goal after two minutes, but Connor Wickham’s double put struggling Sunderland ahead before Samir Nasri snatched a late equaliser.
Manuel Pellegrini’s City stayed third in the table on 71 points from 33 matches, six behind leaders Liverpool with only one game in hand.
Goals from Jason Puncheon and Scott Dann gave Crystal Palace a 2-0 lead at Goodison Park before substitute Steven Naismith pulled a goal back for Everton.
Cameron Jerome’s strike restored Palace’s two-goal advantage before Kevin Mirallas grabbed a late consolation for Roberto Martinez’s side.
Everton’s defeat, which followed a run of seven wins in a row, left them on 66 points from 34 matches, a point adrift of fourth-placed Arsenal with four games remaining.
Having suffered a 3-2 defeat by leaders Liverpool on Sunday, Manuel Pellegrini’s City knew anything other than three points would seriously dent their title hopes and a slick passing move enabled Fernandinho to fire home after two minutes.
With talismanic midfielder Yaya Toure missing through injury, City lacked a cutting edge and Wickham was in the right place on 73 minutes to convert Emanuele Giaccherini’s left-wing cross and score his first Premier League goal since 2011.
City have won just twice in their last eight games against Sunderland and Wickham put Gus Poyet’s side in front on 83 minutes when he beat Joe Hart at his near post.
But Sunderland hopes of a shock victory ended when goalkeeper Vito Mannone spilled Nasri’s shot into his own net with two minutes remaining.
Palace, in search of their fourth consecutive league win, took the lead after 23 minutes when Yannick Bolasie escaped from left back Leighton Baines and put a cross into the box that Tim Howard failed to deal with and Puncheon applied the finish.
Winger Bolasie continued to be a nuisance and he gave Everton another scare when he smashed a 20-metre strike against the base of the post, but Tony Pulis’s were undeterred and they extended their advantage on 49 minutes when Dann headed in from a corner.
Martinez introduced Naismith in the hope of clawing a goal back and it worked as the Scottish striker poked the ball home on 61 minutes.
Jerome restored Palace’s two-goal cushion before Belgium winger Mirallas pulled a goal back for Everton when he clipped the ball past Julian Speroni to set up a grandstand finish but the visitors held on.
(Editing by Ed Osmond)