Zak Coxon and debutant Dara Jikiemi netted for the Reds in the first half of the 80-minute affair.
The scoring was completed after the break by Finn Inglethorpe.
Coxon opened the scoring in the 25th minute with a low finish before the lead was doubled with Jikiemi's header from a corner.
Ryan Cowley, making his first appearance in 20 months, played the opening half an hour and went close to scoring on four occasions.
Liverpool's third arrived in minute 70 when Inglethorpe nodded in a cross from Cian Powney Wain.
