Cherki inspires Man City, Newcastle strike late to reach League Cup semis
City face the Magpies in the last four, while Chelsea will take on Arsenal or Crystal Palace.
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.
"We have had a run of a lot of games for Erling for example and Ruben (Dias) and the other ones and they have to be ready,” Guardiola said.
"We have to do it (give them a rest) and we talked a lot about these days about everyone being connected today."
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 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.
Newcastle ended a 70-year wait to win a domestic trophy when they won the League Cup last season and Howe is eager for more.
"It was important to bounce back from Sunderland, to come back in a positive fashion," he said.
"We want to be competitive and win trophies - this one we had a great experience last year we want to do that again."
Chelsea booked their place in the two-legged semi-finals early next year with a 3-1 win at Cardiff on Tuesday.
Arsenal host Palace in the final quarter-final tie next week.