A goal either side of the break sealed progression to the quarter-finals as the Chilean's side made light work of Jose Mourinho's men, who were second-best throughout
A first-half strike from Stevan Jovetic put last year's finalists a goal to the good, while Mourinho's men looked second-best throughout the contest.
Samir Nasri doubled City's lead after the break and progression was all but sealed, with Joleon Lescott even having a goal disallowed for offside 15 minutes from time.
Following a week in which Pellegrini and Mourinho had engaged in a war of words as the Premier League title race heats up, it was the City boss who won the argument in this fifth-round clash.
|VIEW FROM THE ETIHAD
|By Peter Staunton at the Etihad Stadium
This was a very satisfying measure of revenge exacted by Manuel Pellegrini's side following their recent league defeat to the same opposition.
Goals from Stevan Jovetic and Samir Nasri gave Manchester City the victory they deserved and the bragging rights over Jose Mourinho. This City performance had a lot of positive aspects, including the return of Nasri from injury, and to win such a game without some first-team regulars stands City in good stead with some difficult games to come.
For Jose, however, it's failure... but one less trophy to worry about.
Jovetic redeemed himself a few moments later, though, the Montenegrin finishing off a sweeping team move with a composed low finish that a stranded Cech could do nothing about.
And the Blues stopper was almost picking the ball out of his net again after 23 minutes, forced to produce a diving save to keep out Edin Dzeko's curling effort.
Opportunities gradually dried up, however, as Chelsea began to gain a foothold in the contest, although City were unfortunate not to double their advantage two minutes before the interval when Dzeko only just failed to get on the end of a dangerous low ball from James Milner.
Mourinho made a change at the break, winger Mohamed Salah replacing Samuel Eto'o, but it was City who continued to dictate the pace of the game.
They failed to capitalise on several promising openings in the early stages of the second period but the introduction of Nasri for Jovetic proved instrumental on 67 minutes, as the France international pounced to put Pellegrini's side firmly in command.
The former Arsenal man played a neat one-two with David Silva, who - despite a suspicion of offside - presented Nasri with the simple task of tapping into an empty net to mark his comeback in the perfect manner.
Chelsea got the benefit of the offside flag a few minutes later as Lescott's effort was ruled out after he had pounced on a rebound from Javi Garcia's header, though that decision proved to be little more than a footnote as City coasted to a deserved win that gave Pellegrini something to cheer.