In the second half Liverpool took control of the game with James Frayne scoring the Reds' third and subsitute Ray Putterill adding the fourth near the end.
Coach John Owens said: "It was a good win and performance but we let a couple of daft goals in. It is not the best way to start a game gifting goals. We initially started well, but I was disappointed that we gave away two quick goals, both from errors.
"We played well for the rest of the half and also in the second half. Once we equalised I felt pretty confident we would go on in the second half. Everything was right - the pitch, the conditions and so on - for us to play some good football. And we did.
"We had to wait a week, but it is good to get back on winning ways and we are still playing a good level of football which we now expect of this group."