Despite scoring 13 goals in the previous four games, they struggled in front of goal, but they held on and condemned Bolton to their fourth consecutive defeat.
Disciplined defence prevented Boiton from having the set-pieces which they find so profitable.
Rafa Benitez only made one change to the home side, bringing back club captain Steven Gerrard, who was sent off against Everton.
Trotters manager Sam Allardyce made several changes to the team which lost this week to relegation threatened Birmingham.
He brought Nicky Hunt and Ricardo Gardner into defence as well and Greece international Stelios Giannakopoulos and Gary Speed to add bite to midfield.
The first chance of the game fell to Kevin Nolan but he could not direct it on goal.
A chipped ball from the same player almost gave the visitors the lead, but Jose Reina made a sharp save one-on-one with Giannakopoulos.
Both teams looked positive, but Bolton's aerial strength snuffed out any threat from the home team.
Abdoulaye Faye won himself a yellow card by failing to let go of the ball after a hard tackle on Robbie Fowler.
It wasn't until the half hour mark that Liverpool started to have possession in the opposite half.
John Arne Riise saw a trademark shot go narrowly past Jussi Jaaskelainen's left-hand post and a minute later his deflected cross arrived at Harry Kewell, but he blasted his volley over the bar.
The left flank combination of Kewell and Riise were Liverpool's best option as Gerrard and Xabi Alonso struggled to control midfield.
Liverpool came alive in the 36th minute. The ball came wide to Kewell, who had switched wings, and his cross-cum-shot whistled across the face of the Bolton goal.
Captain Gerrard had a penalty appeal waved away by referee Rob Styles in the 40th minute as the burst into the box, but there was minimal contact.
As the half came to a close the game looked increasingly like a stalemate.
In the 44th minute Peter Crouch looked to have scored after he met Gerrard's cross but his header flew straight to the Bolton keeper.
That was just a reprieve, however. Fowler had a perfect 31st birthday present as he rifled Crouch's knock-down into the bottom right corner deep in first-half injury time.
Liverpool came out strong at the start of the second half looking to build on their lead.
Substitute Luis Garcia created a couple of half chances with neat footwork.
In the 52nd minute a Bolton clearance arrived at Alonso. He created space and struck a fierce shot which came back off the post.
Bolton brought on Henrik Pedersen and Matt Jansen to aid target man Kevin Davies in finding a goal.
They continued to push forward and a goal at either end looked likely.
In the 70th minute Crouch had another clear header in front of goal but it was tame.
Fowler came off to rapturous applause from the Anfield crowd. He was replaced by Dietmar Hamann, as Benitez looked to defend Liverpool's slim lead.
In the 79th minute Ramos Ivan Campo had a strong run into the Liverpool half but he misplaced his final ball.
Kewell counter-attacked from the halfway line in the 81st minute and was clear, but his shot was poor and went wide.
Gerrard had a second appeal for a penalty but referee Styles again thought he had gone down easily.
Bolton tried desperately to gain an equaliser but to no avail.