City were second best for long periods against the relegation-threatened visitors but took the points with a first-half Carlos Tevez penalty and a smart finish by Emmanuel Adebayor after 73 minutes.
The win takes City to 44 points and into fifth place, behind Liverpool on goal difference but with a game in hand on them and fellow challengers Tottenham Hotspur (43).
In other games Fulham beat Burnley 3-0, bottom club Portsmouth grabbed a stoppage-time equaliser for a 1-1 home draw with Sunderland in a game featuring three red cards while Wigan Athletic drew 1-1 with Stoke City.
There are six more games today, highlighted by Arsenal against Liverpool, with Manchester United and leaders Chelsea also in action away to Aston Villa and Everton respectively.
City, who had lost two of their last three league games, struggled to impose themselves at Eastlands although new signing Adam Johnson had a lively home debut.
His tricky running led to the opening goal when he was tripped by Paul Robinson and, though Tevez’s penalty was hit straight at Jussi Jaaskelainen, it had just enough power to creep over the line.
PORTSMOUTH RELIEF
Tevez clipped the bar with a free kick but City rarely threatened another until Patrick Vieira delivered a pinpoint pass into the path of the previously anonymous Adebayor and the Togo striker chested it down and smashed in an excellent goal.
Battling Portsmouth, whose owners are desperately trying to stave off a High Court winding-up order on Wednesday, finally had something to cheer when Aruna Dindane snatched a point six minutes into stoppage time.
Sunderland led with a Darren Bent penalty after 12 minutes, Ricardo Rocha being sent off for the foul and manager Avram Grant following him into the stands at halftime for complaining.
Sunderland were also reduced to 10 when Lee Cattermole collected a second booking eight minutes into the second half and their substitute David Meyler followed him three minutes from time after a straight red.
Sunderland had been on course for their first away win of the season but Burnley are even more hopeless on their travels. Yesterday’s defeat in London left them with only one point from 13 away games and still without an away win in the top flight for 34 years.
Danny Murphy, David Elm and Bobby Zamora were on target for Fulham, who were well worth the victory.
