Pep Guardiola made eight changes from the Premier League win at Sheffield United, but the promotion-chasing visitor never threatened to loosen City's grip on the trophy it won emphatically with a 6-0 Wembley triumph over Watford in May.
Fulham's task, already sizeable, was made practically impossible by the early dismissal of captain Tim Ream as he hauled Gabriel Jesus down for a penalty converted by Ilkay Gundogan.
Bernardo Silva doubled the hosts' lead before the break in the first meeting between the sides in this competition since 1914.
The London club may wish to leave it another 106 years before its next clash with City, which added another two with a quick-fire second-half double from Jesus.
Any hopes Fulham had of springing a shock were dashed after six minutes, Ream pulling down Jesus and Gundogan confidently slotting in the spot-kick.
City naturally dominated and Riyad Mahrez showed great feet before his low shot drew a smart stop from Marek Rodak, while Phil Foden thrashed wide at the end of a swift counter-attack.
The second soon arrived, Silva twisting and turning on the edge of the box before beating Rodak low to his left to bring up City's 100th goal in all competitions this season.
Raheem Sterling replaced Mahrez eight minutes after the restart and the England star clipped the top of the crossbar with his first attempt at goal.
Scott Parker's side, which beat Aston Villa in the previous round, sat deep and was compact, making it difficult for City, but its second-half resistance was ended in the 72nd minute by Jesus's header from Joao Cancelo's cross.
The Brazil striker was then in the right place to nod in the fourth three minutes later after Phil Foden's shot was parried into his path.