Manchester City reignited the Premier League title race as they ended Liverpool's 20-game unbeaten start to the season to reduce their lead at the top of the table to four points.
Pep Guardiola's hosts knew nothing less than a win at Etihad Stadium would do on a Thursday night riddled with tension that produced a game that was frenetic if not a classic.
Leroy Sane produced the decisive moment 18 minutes from time as he collected Raheem Sterling's pass to fire across Liverpool goalkeeper Alisson, after it had seemed like Roberto Firmino's stooping header would maintain the visitors' unbeaten sequence.
Sergio Aguero had earlier given City the lead with a rising, near-post drive just before the interval.
That came after a moment of drama when Reds forward Sadio Mane hit the City post and John Stones scrambled the ball off the line after his attempted clearance struck goalkeeper Ederson - with data subsequently showing the ball had failed to cross by just 1.12cm.
Both sides had chances in a frantic finale but it was City who claimed a crucial win.