Erling Haaland opened the scoring with his 24th goal of the season in the 10th minute but Liverpool equalised through Fabio Carvalho midway through the first half.
Riyad Mahrez restored City’s lead just a minute into the second half but the Blues were again pegged back moments later, this time via the left boot of Mo Salah.
Nathan Ake was City’s eventual matchwinner with a powerful header just short of the hour.
This evening's draw has confirmed we will travel to Southampton for the quarter-final tie in the new year.
A strong City side could have had a dream start when Erling Haaland was played through by Ilkay Gundogan in the first minute. The Norwegian raced on to the ball but miscued his first-time effort, sending it deep into the South Stand.
Our No.9 got behind the Liverpool defensive line again just a few minutes later and squared for Cole Palmer, but the Academy graduate couldn’t divert his strike goalwards.
City sliced through Liverpool’s defence at will in the opening exchanges and it appeared only a matter of time before the deadlock was broken.
It was no surprise when the goal did come, with just 10 minutes on the clock, that it was via the deadly partnership of Kevin De Bruyne and Haaland.
The Belgian found a pocket of space on the left and looped a cross into the middle that Haaland attacked and prodded home with his left boot.
Liverpool warmed into the game and were on level terms in the 20th minute when Fabio Carvalho arrived late into the box to cushion the ball beyond the diving Stefan Ortega Moreno into the bottom corner.
Just as it was in the first half, City were immediately on the attack after the break.
The lead only lasted a matter of moments as, almost immediately after the restart, Darwin Nunez raced down the left and squared for Mo Salah to tap home.
The nature of a knockout cup tie made the remainder of the match an end to end exchange with the international stars of both teams taking it in turns to attack.
The Blues had a let off in the 71st minute when Nunez, sent through from the halfway line, advanced towards Ortega Moreno but dragged his effort wide of the far post.
Tensions ran high as the final whistle approached with defensive midfield counterparts Rodrigo and Fabinho engaging in a tussle that threatened to breakout amongst all 22 players on the pitch.
Instead we maintained our cool and got over the line to keep alive hopes of a seventh Carabao Cup title since 2014.
More than six weeks on from our last competitive fixture, this performance proved just how ready we are for the gruelling second half of the season to come.
Subs: Carson, Walker, Cancelo, Gomez, Robertson
LIVERPOOL XI: Kelleher, Milner (Phillips 38), Gomez, Matip, Robertson, Bajcetic (Fabinho 45), Thiago (Keita 70), Elliott (Henderson 57), Carvalho (Oxlade-Chamberlain 45), Salah, Nunez
Subs: Adrian, Tsimikas, Ramsay, Doak
Man of the match
Kevin De Bruyne – The Belgian does not appear to be suffering any World Cup hangover.
As well as covering every blade of grass on the immaculate Etihad surface, he produced the moments of quality that truly made the difference in this one.
City simply love the Carabao Cup. We have won the competition four times under Pep Guardiola and eight times in total.
Only tonight’s opponents Liverpool, who were also defending champions this season, have lifted the League Cup on more occasions.
Now, we head into the new year as one of only eight teams with a Wembley final still in our sights.
It led to countless chances across all competitions before the World Cup break and had a huge part to play in Haaland’s incredible scoring record.
Barring an hour in Saturday’s friendly with Girona, the pair have barely seen each other in the last six weeks. None of that mattered when De Bruyne picked the ball up on the left after just 10 minutes.
Haaland instinctively knew where the ball would go and so came the first goal of the night and the 22-year-old’s 24th of the season.
Pep Guardiola reaction
"It’s not easy to keep the ball against them, they have a defensive structure that is the most difficult I have faced in my career.
"We were good in everything. They don’t need anything to score and create chances.
"It’s impossible to be better than them for 90 minutes. But I think we made a really good game against them."
What it means
City are through to the last eight of the Carabao Cup for the fifth time in Pep Guardiola’s seven seasons at the Club.
We will face Nathan Jones' Southampton side at St Mary's Stadium, who reached this stage with a 2-1 victory over Lincoln on Tuesday.
The tie will be played in the week commencing 9 January 2023.
Our next assignment is a trip to Elland Road as we restart our Premier League campaign against Leeds United on 28 December.
More than six weeks on from our last league fixture, Guardiola will be looking to get our title challenge back on track in the fixture live on Amazon Prime Video.
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