Pep Guardiola made seven changes from the City side which won 3-0 at Crystal Palace on Sunday but the hosts had little trouble seeing off Brentford who offered very little going forward.
After a slow start under relentless rain, City began to create opportunities, Cherki dragging a shot wide and having another attempt parried away while Oscar Bobb wasted a decent chance after weaving his way into the area.
His tame effort was straight at the keeper and Bobb went off injured in the 19th minute to be replaced by Phil Foden, who himself made way near the end to allow 19-year-old Charlie Gray to come on and make his senior debut for City.
Brentford’s Mathias Jensen forced City keeper James Trafford into a save with a free kick, the only time they really threatened in the first half and in the 32nd minute Cherki opened the scoring for the hosts.
A City corner was headed away but the clearance fell to Cherki outside the area who chested the ball down before shifting it on to his right foot and letting fly with an unstoppable shot into the far top corner.
Cherki pulled out the Erling Haaland robot celebration, and then went to shake hands with the smiling City striker rested on the bench by Guardiola.
City wrapped up the win in the 67th minute when Savinho took the ball into the area and his shot took a wicked deflection off Kristoffer Ajer which sent the ball looping over the keeper.
Newcastle took the lead in the 10th minute when Fulham keeper Benjamin Lecomte pushed a low cross from Jacob Murphy into the path of Yoane Wissa, who marked his first start for the club by slotting home from close range.
Fulham, who had started the brightest before going behind, were level six minutes later with the unmarked Sasa Lukic guiding a header into the corner of the net from Antonee Robinson’s cross.
The home fans were celebrating going ahead in the 65th minute when Fulham’s Joachim Andersen turned the ball into his own net but the offside flag went up.
Lecomte made an added-time save to deny Miley and when the game looked to be heading for a penalty shootout, Miley’s glanced header from the resulting corner sealed Newcastle’s place in the semi-final.