Branislav Ivanovic's first-half strike proved to be the difference in the end but it could have been a very comfortable victory for the visitors with any luck.
The defeat ended City's 20-game unbeaten streak in all competitions and also marked the first time they had not scored at home, in 62 games, since November 2010 during the Roberto Mancini era.
Just after the half-hour mark, Chelsea pressed forward in search of an opener and it came when Ramires' effort was blocked with the ball falling to Ivanovic on the edge of the area for him to sweetly fire home a left-footed effort from the right side of the box.
That came prior to Samuel Eto'o rifling into the woodwork which wasn't the only time the goal frame denied the Blues as Nemanja Matic saw a thunderbolt cannon into the corner while Gary Cahill's header struck the upright.
Chelsea were reasonably at ease throughout although City did come hard in the dying stages in search of an equaliser.
Nevertheless, Mourinho's side got the job done at Eastlands as they join Manuel Pellegrini's City on 53 points, two behind league leaders Arsenal.
2013/14 Barclays Premier League season scores
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