In what was a fiercely-contested match, Branislav Ivanovic netted with a 20-yard strike to give his side the advantage, and the Blues deserved to add to their tally during a superb performance.
After hitting the woodwork on three occasions, Chelsea gave City opportunities to equalise, but Jose Mourinho's men held out for what could prove to be an important victory in the title race.
Below, Sports Mole takes a look back at the encounter at the Etihad Stadium.
On target: 3
On target: 6
Was the result fair?
Yes. Chelsea delivered one of the performances of the season at the Etihad Stadium, and it would have been a considerable injustice if City had stolen a point in the closing stages. It's unlikely that anyone will witness a better defensive display this campaign, while Eden Hazard and Willian were simply mesmeric in attack. City performed solidly enough, but they were no match for a Chelsea side who illustrated their title credentials with an incredible show of determination.
Manchester City's performance Manuel Pellegrini's men will be criticised for failing to deliver on the big occasion, but they were outworked by their opponents and that was their undoing. They had their chances throughout the 90 minutes, but they looked weak at the back and the visitors from London could have easily netted three or four goals.
Chelsea's performance Where to start? This was as perfect as it gets. Chelsea could have scored more goals, but aside from that, it was a masterclass from the West London outfit. Gary Cahill and John Terry had a huge influence in defence, Nemanja Matic justified the £21m paid for his signature and Eden Hazard delivered a performance that suggested that he isn't too far away from challenging for the tag of one of the best players on the planet.
Sports Mole's man of the match
Eden Hazard: This could go to a number of players already mentioned, but at times, Hazard was unplayable this evening. He glided past Man City players like they weren't there during the match, and his composure and trickery on the ball ensured that his opponents often looked bewildered. Matic and Cahill ran him close, but the Belgian is staking a serious claim for the Player of the Year award.
Biggest gaffe There was no obvious gaffe, but Mike Dean could be criticised for his failure to send off Matija Nastasic in the closing stages. Oscar was on the halfway line when he was pulled down, but he was through on goal, and on another day, the City defender would have been dismissed.
Referee performance Mike Dean had a difficult job to control a match between two teams who played with a high intensity, and had to make decisions on tackles flying in left, right and centre. It wasn't the perfect 90 minutes, but Dean deserves credit for letting the game flow at the right time and getting the majority of the decisions correct.
Manchester City: Man City face the long journey to Norwich City on Saturday, before entertaining Sunderland at the Etihad Stadium.
Chelsea: The Blues host Newcastle United on Saturday and make the trip to West Bromwich Albion three days later.