Riyad Mahrez's 55-minute strike proved to be the difference as City patiently set about grinding their opponents down.
Up until that point, Eddie Howe's men had shown impressive resilience and structure in holding off the visitors - but it ultimately wasn't enough to prevent the defeat.
City now sit two points clear of Liverpool, who have the chance to reclaim the top spot when they take on Everton at Goodison Park tomorrow.
So how did the two teams fare? See the gallery below for our player ratings.
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