Goals in either half from Liam Millar and Glen McAuley secured the result for Neil Critchley’s side, who thereby exacted revenge for a pair of defeats against the same opponents earlier in the season.
With Steven Gerrard and Rob Jones urging the home side on from the touchline, the young Reds carved out a lead with only 13 minutes on the clock.
Slick build-up along the right flank allowed Neco Williams to send in a cross for Millar – and the striker produced an excellent finish in turning the ball beyond City goalkeeper Arijanet Muric.
The visiting stopper twice prevented Liverpool from extending their lead subsequently, first denying McAuley – played through at the end of a move which started with a superb Liam Coyle tackle to retrieve possession – moments after the opener.