Former Coventry City youngster Danny Sturridge needed only seven minutes to open his goal scoring account for Liverpool.
Sturridge, who joined from Chelsea for £12m was given his Liverpool debut in the FA Cup Third Round tie at Mansfield Town and slipped the ball into the net in the seventh minute.
He was booked and in the 55th minute was substituted by Luis Suarez, who scored the Scousers second with a highly dubious handball four minutes later.
Former City loanee Jordan Henderson also came on for Liverpool before Matt Green pulled one back in the 78th minute as Liverpool won 2-1 and will travel to Oldham Athletic in Round Four.