After falling behind early, the defending champion struck back with two goals to win the match.
Yaya Toure was the match winner as Manchester City emerged from its recent slump with a 2-1 comeback victory over Swansea City.
The Premier League champion came into Saturday's match with just one win from its last six matches in all competitions.
Wilfried Bony made the most of frailties among Manuel Pellegrini's team by handing Swansea an early lead at the Etihad Stadium, but recalled forward Stevan Jovetic restored parity after 19 minutes.
Below-par performances from midfield talisman Toure have often defined City's malaise this term, but the Ivory Coast international showcased his trademark combination of power and poise to net decisively 17 minutes into the second half.
Swansea boss Gary Monk used his substitutions shrewdly to craft a dramatic finish, with replacements Bafetimbi Gomis and Jonjo Shelvey agonizingly close to securing a late share of the spoils.
Pellegrini's men remain eight points behind leader Chelsea, and have closed to within a point of Southampton before Ronald Koeman's second-placed team travels to Aston Villa on Monday.
Captain Vincent Kompany returned from a calf problem for the home team but a similar complaint for Edin Dzeko contributed to Jovetic starting in attack.
Shelvey had to settle for a place on the Swansea bench following a one-match suspension, while Nathan Dyer returned to the starting XI and the winger played a key role in the opening goal after eight minutes.
The champions' defensive vulnerability was on full display when Bony charged onto a return chipped pass from Dyer to coolly slot past Joe Hart.
There was little conviction in City's response until Toure released Jesus Navas and the Spain winger fizzed in an excellent low right-wing cross to leave Jovetic with a simple finish.
Lukasz Fabianski brilliantly tipped a venomous Gael Clichy long-range strike onto the post after 39 minutes, and Pellegrini's men resumed on the front foot after the interval, but a slick exchange of passes between Bony and Jefferson Montero forced Hart into a fine save from the latter.
Fabianksi was unsighted when Toure drilled goalwards in the 61st minute - he got down well to save but had no chance when the same player put Pellegrini's side ahead little more than a minute later.
Tom Carroll was careless in possession, allowing Samir Nasri to find Fernandinho in the Swansea box and his midfield partner charged onto a perfectly weighted backheel to prod home.
Navas became the latest attacker to be frustrated by Fabianski but late nerves afflicted City as Gomis spurned an 87th-minute one-on-one and Shelvey's deflected free kick spun wide with Hart beaten.
City will certainly require far more poise in Tuesday night's must-win UEFA Champions League clash with Bayern Munich.