The Reds scored three times in a stirring eight-minute spell in the second half to go 4-1 up, at that point clung on after City scored twice over the most recent six minutes.
Jurgen Klopp's side - playing their first diversion since Philippe Coutinho's £142m move to Barcelona - merited their triumph as they finished City's expectations of experiencing the association season without losing, and stretched out their own unbeaten hurried to 18 recreations.
Alex-Oxlade Chamberlain's low drive gave Liverpool an early lead, yet City were level before half-time through Leroy Sane, who beat Loris Karius at his close post following Joe Gomez's error.
The diversion handed definitively over two minutes either side of great importance stamp, when poor protecting by John Stones let in Roberto Firmino, and Sadio Mane - who had recently hit the post - struck a dazzling completion high past Ederson.
Ederson's poor freedom talented Mohamed Salah a fourth, and regardless of their late wobble, Liverpool finished off the win to go third in the table.
While the Reds' main four test goes from quality to quality, City can in any case consider a 15-point lead over Manchester United, who have Stoke on Monday.