Manchester City s Algerian midfielder Riyad Mahrez celebrates scoring the opening goal during the English Premier League football match between Chelsea and Manchester City at Stamford Bridge in London on January 5, 2023. Photo: AFP
Pep Guardiola's men were well below par in the first half but were transformed after the break, with substitutes Jack Grealish and Riyad Mahrez combining for the only goal, scored by the Algerian in the 63rd minute.
Graham Potter's Chelsea came into game languishing in 10th place in the table and were expected to face a searching examination from second-placed City but they had the better of the first half.
Chelsea, however, were up against it from the opening minutes, with forward Raheem Sterling forced off after suffering an apparent hamstring injury, replaced by Pierre-Emerick Aubameyang.
Potter was also without a string of senior players including Mason Mount, Reece James, Ben Chilwell and N'Golo Kante.
The game at Stamford Bridge was scrappy in the initial stages, with the visitors dominating possession but creating little of note.
Chelsea were first to threaten, in the 16th minute, but City defender John Stones came to the rescue as Christian Pulisic bore down on goal, producing a perfectly timed sliding tackle to deny the US forward.
The American was injured in the challenge and was forced off minutes later, compounding Chelsea's problems.
Teenager Carney Chukwuemeka, who came on for Pulisic, almost made an instant impact, but his shot was blocked and Hakim Ziyech's effort was saved by City goalkeeper Ederson.
Erling Haaland, who has one more Premier League goal this season -- 21, than the entire Chelsea side, smashed a shot wide in the 38th minute.
But Chelsea continued to look the more dangerous side and came agonisingly close to breaking the deadlock when Chukwuemeka hit the post in the 44th minute.
Guardiola made a double substitution at half-time, bringing on Rico Lewis and Manuel Akanji for Joao Cancelo and Kyle Walker in the search for more control.
The visitors immediately settled and began to dictate play, with Nathan Ake heading against the woodwork, but Chelsea responded well and were inches away from taking the lead when Thiago Silva flashed wide.
Guardiola brought on Grealish and Mahrez on the hour mark to further freshen up his attack.
The decision paid dividends minutes later when Grealish produced an excellent pass from the left and Mahrez prodded home from close range.
Potter made changes of his own, including bringing on England forward Conor Gallagher, but they were unable to find an equaliser despite some late pressure.
The result leaves City five points behind Arsenal, who dropped points in a 0-0 draw against high-flying Newcastle earlier in the week.
Chelsea now have just one win in their past eight league games and remain 10 points off the top four.
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