Pep Guardiola’s men began well at a wet and windy Etihad Stadium and took the lead just after the half-hour mark with a stunning Cherki strike.
The Frenchman was loitering on the edge of the box from a corner, and when the ball was headed out into his direction, he expertly got the ball under control and thundered a ferocious strike into the top corner.
The visitors emerged from the interval with an attacking intent and forced James Trafford into a smart stop to deny Kristoffer Ajer eight minutes after the break.
Just after the hour mark, Phil Foden almost doubled our advantage, but his half-volley from 12 yards was expertly saved by the sprawling Brentford goalkeeper Hakon Valdimarsson.
Four minutes later, we did double our lead, with Savinho leading a swift counter attack and seeing his shot deflect off the sliding Ajer and loop over Valdimarsson and into the net.
Academy star Charlie Gray came on inside the final 10 minutes for his senior debut as we cruised into the last four of the competition.
View the best images from the victory via our gallery below.