The champions went ahead through a 78th-minute header by David Luiz and a late Ramires strike sealed a victory which moved Chelsea above their opponents into third place in the table.
Chelsea are nine points behind leaders Manchester United with a game in hand and still have to play them at Old Trafford.
They have 54 points, one point and one place above City with a game in hand. Arsenal are second on 58 points with United top on 63 after their last-gasp 1-0 win over Bolton Wanderers on Saturday.
Liverpool won 2-0 at Sunderland in Sunday's other match.
The exciting finale to the game at Stamford Bridge was out of keeping with what had gone before.
The teams boasted the best defensive records in the division and it was no surprise that the match was a cagey affair with neither side prepared to take too many risks.
Chelsea made most of the running but struggled to create any clear chances, Florent Malouda side-footing the best weakly at Joe Hart early in the second half.
With little sign of a breakthrough coming manager Carlo Ancelotti sent on Didier Drogba and Nicolas Anelka for the last 20 minutes and removed the largely anonymous Fernando Torres who is still seeking his first Chelsea goal since his record move from Liverpool.
IMMEDIATE IMPACT
Drogba made an immediate impact when he swung over a free-kick from the right and Brazilian defender Luiz nodded in from close range to further increase his popularity with the Chelsea fans following his vital recent goal against Manchester United.
City, without the injured Carlos Tevez, were unable to muster any sort of response and never looked capable of making it four wins in a row over the Londoners.
Instead it was Chelsea who broke clear in stoppage-time as Ramires skipped through some half-hearted tackles before planting the ball beyond Hart.
"We had to be quicker up front (in the second half) and find the right solution in the final third," Ancelotti told Sky Sports
"I think City lost a bit of power in the second half but I was very happy with our performance."
The result completed a miserable week for City, who were knocked out of the Europa League by Dynamo Kiev on Thursday.
"We played three days ago with 10 players and in the last 25 minutes we were so tired," said coach Roberto Mancini.
"After yesterday's results a win or a draw today would have been fantastic but we have eight games to go so it's very important to recover all the players and maybe without the Europa League we can prepare very well for them."
Liverpool maintained their chase for a Europa League slot as a fortunate Dirk Kuyt penalty and a great goal by Luis Suarez secured a comfortable victory at Sunderland.
