63’ (pen)
Ilkay Gundogan scored two second-half goals as Manchester City claimed a top-flight record-equalling 14th successive win in all competitions with a 4-1 victory at Liverpool.
City were handed an opportunity to break the deadlock on 37 minutes when Sterling drew a foul from Fabinho, but Gundogan fired his penalty over.
Gundogan made amends for his miss four minutes after the restart, lashing in the rebound after Alisson parried Phil Foden's shot.
Liverpool equalised on 63 minutes, Mohamed Salah making no mistake from the penalty spot with a thumping finish after the Egyptian had been fouled by Ruben Dias.
But Man City struck three times in 10 minutes to secure victory.
Gundogan was played in by Foden to convert from close range after a defensive mix-up on 73 minutes before Sterling's diving header from a poor Alisson clearance made the score 3-1.
Foden completed the scoring in style with a sizzling strike as Pep Guardiola claimed his first win as a manager at Anfield.
City move five points clear of second-placed Manchester United and with a match in hand. Liverpool remain fourth, 10 points behind City.
See: Liverpool report | Man City report
Next fixtures
Liverpool: 13 Feb v Leicester (A)
Man City: 13 Feb v Spurs (H)
Match officials
Referee: Michael Oliver. Assistants: Stuart Burt, Simon Bennett. Fourth official: Chris Kavanagh. VAR: Paul Tierney. Assistant VAR: Constantine Hatzidakis.
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