Manchester City's goalkeeper Stefan Ortega dives but fails to save the goal from Liverpool's Fabio Carvalho (second right) during the English League Cup soccer match between Manchester City and Liverpool at Etihad stadium in Manchester, England on Dec 22, 2022. (JON SUPER / AP)

MANCHESTER, England - Manchester City beat League Cup holders Liverpool 3-2 in a cracking game on Thursday, taking the lead three times before holding on to reach the quarter-finals.

Erling Haaland scored his 24th goal of the season in all competitions to put City ahead in the 10th minute at the Etihad Stadium but Liverpool responded in the 20th, when Fabio Carvalho knocked in a James Milner pass to complete a flowing move

Defender Nathan Ake headed in what proved to be the winning goal in the 58th minute after Mohamed Salah had equalized one minute after Riyad Mahrez restored City's advantage early in the second half.

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Erling Haaland scored his 24th goal of the season in all competitions to put City ahead in the 10th minute at the Etihad Stadium but Liverpool responded in the 20th, when Fabio Carvalho knocked in a James Milner pass to complete a flowing move.

It was another fast and furious game between the two rivals who took the Premier League title race to a dramatic conclusion last season and, as then, it was City who finished on top.

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They will travel to Southampton in the quarter-finals.

Liverpool coach Juergen Klopp thought Haaland's goal was offside and lamented the fact VAR technology is not used in the League Cup until the semi-final stage.

"We have VAR, the referees are used to VAR. The technology is here, why shouldn't we use it?," said the German coach.

"We worked hard, we did good stuff. It was not good enough for tonight but it's City at their home ground, it will always be an incredibly difficult game."

City coach Pep Guardiola, who enjoyed a first win over Liverpool in six matches in all competitions, was pleased with his side's performance.

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"We cannot say it was not a good game," he said. "It's not easy to keep the ball against Liverpool because they have a defensive structure that is the most difficult I ever faced in my career."

Haaland looked refreshed from his extended break due to Norway's failure to qualify for the World Cup and heavily contributed to his team's build-up play, setting up a great chance for Cole Palmer but the youngster sliced his shot wide.

Manchester City's Kevin De Bruyne (right) makes an attempt to score during the English League Cup soccer match between Manchester City and Liverpool at Etihad stadium in Manchester, England on Dec 22, 2022. (JON SUPER / AP)

Haaland had no such problem when presented with his first clear chance, stretching out his left leg to send Kevin De Bruyne's cross into the net.

City's defense switched off and allowed Liverpool to pass their way around their area and equalise through Carvalho.

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Guardiola's side looked more likely to score again and did so soon after the interval, Mahrez controlling a through ball from Rodri with one foot and slamming it low into the net with the other.

As has often been the case in the recent years of the fixture, though, Liverpool came straight back and Darwin Nunez made a lung-bursting run down the left wing to latch on to a pass and sent it across for Salah to tap in.

City would not be outdone, however, and took the lead for the final time, Ake rising high to head home an inviting cross from De Bruyne.