The triumph marked Enzo Maresca's sixth consecutive league win, making him the fourth manager to achieve the feat at the start of a Premier League managerial spell.
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City moved three points clear of Arsenal with 18 points, while Liverpool remained ninth on seven.
After a goalless first half, Liverpool's hopes suffered a major setback when Ryan Gravenberch received a second yellow card for fouling Jeremy Doku.
Erling Haaland broke the deadlock in the 65th minute, capitalising on a blocked effort from Doku.
Three minutes later, Doku curled home a stunning second before Rayan Cherki completed the scoring with a clinical finish.
The result strengthened City's grip on top spot and extended their winning streak to six matches.