Second half goals from Emile Heskey and a Danny Murphy penalty were enough to ensure progression into the fourth round of the Cup for Gerard Houllier's men but only after surviving a real scare in the first half.
Yeovil showed no signs of nerves and attacked Liverpool from the outset with some fine passing moves to put The Reds on the backfoot.
The Division Three side created the first noteworthy effort of the game on 17 minutes with Darren Way blazing over the crossbar from just inside the box after a neat flowing move down the right.
Liverpool created their first chance of the contest six minutes later when El Hadji Diouf swung over a cross from the left to Vladimir Smicer, but his header lacked the power to beat Chris Weale.
Yeovil came closest to breaking the deadlock on 25 minutes when the ball broke to Gavin Williams on the edge of the area and he fired in a stinging shot which forced Jerzy Dudek to fling himself across goal to push round the post.
Seconds later Yeovil threatened the visitors' goal again with Way finding himself free at the far post, but Liverpool were able to get players across to smother the danger.
The visitors almost opened the scoring against the run of play three minutes before the break when Smicer broke free down the right and pulled the ball back invitingly for Diouf, but the Senegal star could not get his shot on target.
Liverpool came out in determined fashion in the second half and substitute Heskey forced Weale into a good block with a close-range shot after being played through by Sami Hyypia.
The visitors were now in dominant mood and were unlucky not to score after 63 minutes when Smicer fired in a shot from the edge of the box which beat Weale, but came back off the post much to the home side's relief.
Liverpool finally made the breakthrough their dominance warranted on 70 minutes when Murphy and Harry Kewell swapped passes before Murphy picked out Heskey in the box and the striker kept his cool to fire past Weale.
The Premiership side put the game beyond doubt six minutes later when Murphy converted from the spot after Kewell was brought down by Hugo Rodrigues inside the box.
Yeovil refused to give in and Terry Skiverton should have done better on 79 minutes when he beat Stephane Henchoz at the back post, but he could not get his header on target.
Substitute Kirk Jackson also went close seven minutes from time with a fine shot on the turn which forced Dudek into an acrobatic stop.
