Adam Sadler's team were looking to keep up their position at the top of the League, while the visitors were keen to bounce back from a 2-1 defeat at Bolton Wanderers.
It was a tentative start, with both teams determined to impose themselves. City kept possession and attacked with confidence, but struggled to create any clear-cut chances against a well-organised Liverpool side.
Then with 29 minutes gone, the ball fell in the box for Matthew Regan, who blazed wide from five yards. It was a glaring miss for the visitors, but all was forgiven when Liverpool took the lead just minutes later.
Midfielder Jack Dunn ran down the left and passed to David Moli, who fired home to punish City's lapse in concentration after being caught on the break.
Liverpool might have made it two before the break but Regan's glancing header from an inswinging corner went just wide of the post
The second half offered little solace for City as the visitors doubled their lead with a stunning strike from the edge of the box by Jordan Lussey.
With 71 minutes gone the Blues were offered a lifeline from the spot after luckless defender Regan handled. Albert Rusnak stepped up but Tyrell Belford produced a solid save to deny City a route back.
The Blues didn't give up and continued to push for an opening, but Liverpool stood firm and scored a third, with Dunn confidently slotting the ball over home keeper Angus Gunn. Further blows were dealt to the home side with the loss of star players Alex Henshall and Albert Rusnak through injury.
City did get a goal back through leading scorer Jordi Hiwula, but with only five minutes to go it was merely a consolation for a Blues side that was well beaten in the end by the impressive visitors.