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.
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.
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.
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.
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.
