Defender Luiz put a clutch of the world's most expensive strikers to shame by breaking the deadlock late on before Ramires wrapped up the points in stoppage-time.
The win lifted Chelsea above City into third place and back within nine points of Manchester United with a game in hand, while City are now 10 adrift having played the same number of matches.
A goal finally came as Luiz earned a 77th-minute free-kick wide on the left, Didier Drogba whipped the ball in and the Brazilian glanced a header through the fingertips of Joe Hart.
Luiz went close to converting another free-kick from Drogba, and City threw men forward but they were killed off in the second minute of stoppage time when Ramires danced through their defence before clipping beyond Hart.
There was still time for Luiz to blot his copybook with a late caution but the points were already secure.
Source: PA
Source: PA