Ahead of the hectic festive Premier League schedule, Pep Guardiola could afford to give Erling Haaland the night off as his side secured a sixth consecutive victory in all competitions.
Haaland was left on the bench among seven changes by Guardiola at the Etihad.
Abdukodir Khusanov was one of those handed a rare start and the Uzbek defender was lucky just to see a yellow card for chopping down Kevin Schade when the German looked set to run through on goal.
Guardiola was forced to field the in-form Phil Foden for longer than he hoped as the England international replaced the injured Oscar Bobb after just 20 minutes.
But it was Cherki who unlocked the Brentford rearguard action in style 10 minutes before half-time.
The Frenchman collected a corner cleared to the edge of the box, cut inside onto his right foot and unleashed an unstoppable effort into the top corner.
The home side’s second was much more fortunate as Savinho’s shot looped over Hakon Valdimarsson via a deflection off Kristoffer Ajer 20 minutes from time.
City won the League Cup four years in a row under Guardiola between 2018 and 2021.
But this is the first time in five seasons they have progressed to the last four.
Newcastle, meanwhile, are back in the semi-finals thanks to Lewis Miley’s stoppage time header at St. James’ Park.
A dismal performance in losing 1-0 to local rivals Sunderland on Sunday heaped the pressure on Eddie Howe’s men to respond.
Yoane Wissa opened his Newcastle account on his first start after just 10 minutes but Sasa Lukic quickly levelled for the visitors.
The tie appeared destined for penalties until Miley got a flick to Sandro Tonali’s enticing delivery.
Arsenal host Crystal Palace in the final quarter-final tie next week. (AFP)