Liverpool made a fast start and were deservedly ahead when Trent Alexander-Arnold fired past Ederson.
City were much improved after the second half and substitute Julian Alvarez equalised from close range after Phil Foden had caused panic in the Liverpool six-yard box.
But a late Mo Salah penalty and an injury-time header from Darwin Nunez sealed the victory for Liverpool.
You can watch extended highlights of the game above.
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You can receive comprehensive coverage of every single City match on the official Man City app.
Two hours before kick off, our Matchday Centre will begin providing live text updates, gathering together all the latest team news, stats, analysis and quotes.
And then just before the teams are announced, Matchday Live will begin, with former City players joining us in the studio to offer their insight.
Highlights are available free and CITY+ subscribers can also watch a full 90-minute replay of every single game from midnight.
