Liverpool started the brighter, with Jimmy Ryan coming close to opening the scoring after nine minutes but his fierce drive went narrowly wide. Ryan soon found his sights however, and cleverly flicked the ball home after some good wing play from Ray Putterill.
The goal sparked Chelsea into life but although they put Liverpool under plenty of pressure, goalkeeper Martin Hansen didn't really have a lot to do in the first half.
Chelsea started the second half like they ended the first but again failed to put Hansen under any real pressure. All the best chances after the interval were Liverpool chances.
Craig Lindfield and Lee Woodward saw chances go narrowly wide before Ray Putterill killed the game off with a deserved goal in front of the Kop.
Liverpool will meet the winners of the Coventry-Reading game in round five.