Ilkay Gundogan converted the resulting penalty before Bernardo Silva’s smart turn and shot quickly doubled City’s advantage.The visitors then held out for nearly an hour but two headers in three minutes from Jesus gave the scoreline a more accurate reflection of the English champions’ dominance.
Pep Guardiola’s men have now won 17 domestic cup ties in a row.
The Catalan is relying on more cup success for silverware this season after conceding the Premier League title is beyond his side with Liverpool 16 points clear at the top of the table.
Guardiola made eight changes to the team that won 1-0 at Sheffield United in midweek, but still named a strong side with both David and Bernardo Silva and Gundogan among those coming into the team.
Fulham boss Scott Parker also rotated with his priority securing a return to the Premier League at the first time of asking.
Any hope of an upset was quashed within minutes by a rash challenge from Ream.City have had problems from the spot this season with Guardiola even claiming goalkeeper Ederson is his best taker after Jesus’ latest miss at Bramall Lane on Tuesday.
However, with the Brazilian on the bench with Claudio Bravo keeping his starting spot in goal for the cups, it was Gundogan who took responsibility to dispatch the spot-kick.
A moment of magic from Bernardo then gave the hosts breathing space as the Portuguese international fired into the bottom corner from outside the box.
Only a lack of killer instinct prevented City from further running up the score as Raheem Sterling came off the bench to hit the crossbar.
Jesus, though, bagged a confidence-boosting double by heading home Joao Cancelo’s cross before nodding in the rebound after Marek Rodak had saved Phil Foden’s initial effort.