Prior to the match Mancini had threatened to drop Hart if he continues to make mistakes and had also complained about some players only giving '50 percent' but he could have none after the win.
City kept their second spot but this win won't have any significance in the title race. Chelsea were second-best throughout the game, falling to second half goals from Yaya Toure and Carlos Tevez. Rafa Benitez's side managed only two shots on target and one of those was Frank Lampard's penatly, which was saved by Hart.
Hart was lucky to stay on the pitch after bringing down Demba Ba in the area. Referee Andre Marriner pointed to the spot but did not produce a card.
Just three short of Bobby Tambling's club record, Lampard shoul dhave scored having converted his last 10 penalty attempts. But Hart moved to his right even before Lampard had taken the shot.
The first goal finally arrived in the 63rd minute after David Silva fed Toure on the edge of the box. The Ivorian tricked past Lampard and John Obi Mikel before his right-foot shot curled inside the far post.
Tevez came on as a substitute for young Jack Rodwell and sealed three points in the 85th minute. Silva fed Tevez and the Argetine smashed the ball between two defenders and keeper Petr Cech.
Chelsea still keep their third spot but are likely to go down to fourth if their Rivals Tottenham get the better of West Ham on Monday night. The Blues, however, will go head-to-head with other clubs for a Champions League spot.