Stevan Jovetic and Samir Nasri got the goals for last season's beaten finalists, who will be hoping to go one better in 2014 as part of an historic quadruple.
A flowing move which started on City's left flank delivered the opening goal of the game on 16 minutes, with Edin Dzeko threading the final pass through for Jovetic to drill across Petr Cech and in off the base of the post.
City doubled their advantage on 67 minutes, with David Silva beating the offside trap to square for Nasri, who had only been on the field for six minutes, to tap into an empty net.
The presence of John Obi Mikel for John Terry aside, the Chelsea side was identical to the one which beat City 1-0 in the Premier League less than a fortnight ago, after Gary Cahill passed a fitness test.
Yet they lacked the same fluency and although the opening exchanges were cagey, City gradually began to assert themselves and take control.
They served warning of their threat for the first time after 15 minutes as Yaya Toure tested Cech from 25 yards.
The goalkeeper was unable to keep hold but Jovetic reprieved him as he clipped the rebound onto the top of the bar.
There was no let-off a minute later as City pieced together a flowing move, with Silva threading the ball through for Dzeko.
The Bosnian turned instantly to sweep the ball into the path of Jovetic, who steadied himself before guiding an inch-perfect first-time shot past Cech and in off the far post.
Costel Pantilimon, back in City's goal in place of Joe Hart as Pellegrini continued his cup rotation policy, had an anxious moment as Chelsea tried to respond.
The Romanian failed to take a low cross cleanly and eventually dived on it at the second attempt amid confusion in the area.
City stepped up the pressure with Toure dragging a long-range shot wide and Dzeko forcing a good save from Cech with a curling effort from the edge of the box.
Jovetic also turned well outside the area but could get no power on his shot.
Chelsea were struggling to create anything meaningful although Eden Hazard, City's chief tormentor last time out, did wriggle free to get in a shot.
Hazard was also hauled down by his Belgium captain Vincent Kompany as he attempted to engineer another opportunity.
City almost doubled their lead before the interval after Jovetic beat David Luiz to a 50-50 ball to release James Milner.
Milner tore down the right and whipped in a dangerous low ball across the box, but the sliding Dzeko narrowly failed to connect.
Jose Mourinho sent on new signing Mohamed Salah for the second half, in place of the quiet Samuel Eto'o, but the Blues were still unable to trouble the hosts in the final third.
City looked the more fluid and Jovetic almost broke through, but he lost control and went to ground as he passed Luiz and was booked for diving.
With the spark still lacking, Mourinho sent on Fernando Torres for Ramires after an hour's play.
Pellegrini also made a change, sending on the fit-again Nasri for his first appearance in five weeks in place of Jovetic.
Mourinho's frustration became apparent as his team continued to struggle and the Portuguese manager showed further displeasure as decisions went against him.
Nasri's impact was almost immediate as he charged into the box and played a brilliant one-two with Silva to his left and diverted the return ball home.
City thought they had a third goal after a 75th-minute corner, when Joleon Lescott pounced on a Cech fumble from a powerful Javi Garcia header, but the flag was raised for offside.
Willian then made way for Oscar as Mourinho, who was barracked by the City fans, made a last attempt to salvage the match, but it was too little too late as City held firm.
|Manchester City||Team Statistics||Chelsea|
|1||1st Half Goals||0|
|6||Shots on Target||0|
|5||Shots off Target||2|
|51.4||1st Half Poss.||48.6|
|61.2||2nd Half Poss.||38.8|