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.
City, last year's runners-up, rarely looked troubled as they secured their place in the quarter-finals with a dominant display at the Etihad Stadium.
Stevan Jovetic put the hosts in front after 16 minutes with his fourth goal since joining from Italian side Fiorentina in July.
And victory was secured in the second half as midfielder Samir Nasri scored on his first appearance since suffering a knee injury against Newcastle United last month, while City could even afford to see Joleon Lescott's late effort ruled out for offside.
City started brightly and should have taken the lead after 15 minutes when Jovetic hit the crossbar from close range after Chelsea goalkeeper Petr Cech had spilled a drive from Yaya Toure, who was included in the starting XI after the FA decided not to ban him for a kick on Ricky van Wolfswinkel in last weekend's Premier League clash with Norwich.
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.
Cech 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 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, but that decision proved to be little more than a footnote as City coasted to a deserved win that gave Pellegrini something to cheer.
