Nathan Ecclestone and Lauri Dalla Valle had tested the goalkeeper before Amoo's breakthrough and the pairing continued to work the Chelsea keeper throughout.
Dean Bouzanis in the Reds goal was beaten once on the night but luckily the linesman had already flagged for offside. Dalla Valle also saw a goal ruled out for offside and again there weren't many arguments.
Despite the scoreline being close, Liverpool were the better team throughout with a much improved performance over the fourth round game with Bristol Rovers and it was a deserved win for Hugh McAulley's side.