Having made five changes from the midweek draw at Lyon in the Champions League, an under-strength City side was pegged back by Callum Wilson's equalizer on the stroke of halftime at Etihad Stadium. But Sterling regained the lead for City in the 57th minute by netting a rebound from close range, becoming the first player to score in his first six Premier League appearances against a single opponent.
Ilkay Gundogan tapped in Leroy Sane's cross for the crucial third goal for City in the 79th as the leaders won a sixth straight game. It was not the most convincing performance from City, which really got on top only after Sterling's goal, but the result piles the pressure on second-place Liverpool ahead of its Merseyside derby against Everton on Sunday.
City was without record scorer Sergio Aguero because of muscle fatigue — the striker was pictured drinking tea in a corporate box during the match — while manager Pep Guardiola started David Silva and Riyad Mahrez on the bench and rested defenders John Stones and Kyle Walker completely. Kevin De Bruyne and Benjamin Mendy remained out injured.
City went ahead after 16 minutes as Leroy Sane raced on to a lofted pass from defense. The ball ran loose as Asmir Begovic came out to meet the Germany winger but Bernardo Silva was on hand to sweep home.
Yet from what seemed a position of control, City uncharacteristically switched off in the latter stages of the first half, allowing Bournemouth back into the game. Wilson almost got on the end of Joshua King's cross and the pair combined for another chance moments later. The hosts failed to take heed and were punished in the 44th minute as Wilson met Simon Francis' cross with a firm header that looped beyond Ederson.
City was almost caught out again after the break but King hesitated in a shooting position and the home side survived. City was also forced to replace left back Oleksandr Zinchenko after his nose was bloodied in a collision with teammate Fernandinho, but the team soon picked up the pace.
Sterling jinked his way through the area and was unlucky to see his shot deflected against the post but he did score soon after. The England forward first teed up a chance for Danilo and then followed up to tuck home after the Brazilian's strike was parried by Begovic.
City threatened more, with Gabriel Jesus forcing a save from Begovic with a good header and Fernandinho dragging an effort wide. Gundogan put the result beyond doubt 11 minutes from time, tapping home from six yards after Sane and David Silva combined to pull the Bournemouth defense apart following a corner.
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