Young Spaniard Brahim Diaz – one of 10 changes to the starting line up – scored his first competitive goals for the holders, who will now face either Leicester or Southampton in the next round.
The League Cup is a time for the Club’s young stars to shine, and Diaz and Phil Foden were in sparkling form at the Etihad.
Diaz was a live-wire presence down the right all evening, while Foden produced another hugely promising performance in central midfield, gliding past players and linking play beautifully.
And although the team was almost completely changed from the win over Spurs at Wembley – John Stones started both matches – City’s dominance of possession and chances remained intact.
When you combine that firepower with a seriously miserly defence – this was a fifth straight clean sheet – then you have a winning formula. The only worry on the night was De Bruyne's withdrawal late on after Fulham player Timothy Fosu-Mensah appeared to land heavily on the Belgian's knee.
After a minute’s silence for the victims of the Leicester City helicopter tragedy play got underway in sharp conditions, with City setting up in a 4-3-3 formation.
Guardiola’s men were quickly into their rhythm, with Sane, Foden and De Bruyne seamlessly syncing down the left.
The first goal came from a corner from that side that was initially worked short before Fabian Delph swung the ball into the box. Vincent Kompany nudged the ball back into the danger zone, where Diaz’s shot deflected in off Aleksandar Mitrovic.
The goal energised City, but despite numerous chances the advantage remained at one. The pick of the moves involved great interplay from De Bruyne and Foden, but Sane sliced his shot.
Just before the break Foden himself went close but his glancing header slid agonisingly just inches wide.
City continued to boss the game after the restart, with Jesus displaying hard work and skill in equal measure - even though a goal eluded him. The Brazilian did, however, play a key role in Diaz' second.
Jesus surged forward and after his shot rebounded off the post, Diaz was on hand to gleefully smash the ball high into the net.
For the record, the VAR system was in use for the first time at the Etihad. Thankfully it wasn’t needed.
Star man - Brahim Diaz
The Spaniard put in an excellent performance on the right wing, arriving perfectly for both of his goals.
Young goalkeeper Aro Muric started in goal for the first time at the Etihad – Claudio Bravo remains a long-term absentee with an Achilles injury – behind a back four of skipper Kompany, Danilo, Oleks Zinchenko and Stones. Stones was the one player to keep his place from the win over Spurs on Monday night.
De Bruyne, Fabian Delph and youngster Foden made up a powerful-looking midfield trio. The game came too soon for Ilkay Gundogan as he closes on a return from a hamstring strain.
Young Spanish ace Diaz took his opportunity on the right flank, along with left winger Leroy Sane and striker Gabriel Jesus,
City's bench contained an array of talent, including young French midfielder Claudio Gomes, who replaced De Bruyne for the final few minutes.
City face three home games in quick succession against Southampton (Sunday 4 November, 3pm, Premier League), Shakhtar Donetsk (Wednesday 7 November, 8pm, Champions League) and Manchester United (Sunday 11 November, 4.30pm, Premier League).