Second half goals from Emile Heskey and Patrik Berger were enough to give Liverpool all three points after Nick Barmby sensationally gave The Reds the lead only for Kevin Campbell to equalise for the visitors.
Everton had started the game the better and they wasted a glorious chance to take the lead after just five minutes. Mark Pembridge lobbed the ball wide after being set-up by Campbell and he was made to rue his miss when former Everton star Nick Barmby gave the home side the lead.
England midfielder Barmby, who moved across the city from Goodison in the summer, netted on 12 minutes to silence the Everton boo boys and send the home fans wild.
Christian Ziege sent over a cross from the left which was deflected to Barmby unmarked at the far post, who headed home brilliantly past Paul Gerrard in front of the Everton fans at the Anfield Road End for his first league goal for his new club.
Just a minute later Welsh midfielder Pembridge should have drawn the visitors level but he dragged his shot wide after being put clear on goal.
Everton did get a deserved equaliser when Campbell, who scored the winner in the corresponding fixture last season popped up on 17 minutes, stooping to head home after David Weir had headed back an Idan Tal corner at the far post.
Barmby almost restored Liverpool's lead five minutes before the interval, but he missed Emile Heskey's cross in the six-yard box.
Then Finnish defender Sami Hyypia saw his header well saved out by Everton keeper Paul Gerrard on the stroke of half time and both sides went in level at the break.
Liverpool were far more committed in the second half and they started to totally dominate the proceedings with Gary McAllister and Dietmar Hamann taking a grip on midfield which was run by the impressive Paul Gascoigne in the first 45 minutes for Everton.
The home side almost restored their lead after 50 minutes when Dietmar Hamann exchanged passes with McAllister and ran from half way down the right unopposed, and fired in a low drive which Gerrard did well to save.
Everton boss Walter Smith then replaced the injured Michael Ball with Gary Naysmith after 53 minutes and within three minutes he found his side 2-1 down thanks to a goal from the in-form Emile Heskey.
Heskey netted his sixth goal in four games to put Liverpool back in front shooting powerfully home from 25 yards after the ball broke loose to the in-form striker when Barmby appeared to be fouled.
Vladimir Smicer replaced Robbie Fowler after 68 minutes and it was the Czech midfielder who played a major part in the third and final goal.
He latched onto a long throw from Sander Westerveld and raced clear of the Everton defence and Thomas Gravesen brought the player down inside the penalty area as he tried to shoot.
Referee Paul Durkin pointed to the spot and sent off the Danish international midfielder for the professional foul.
With Robbie Fowler off the pitch Patrik Berger took over the penalty taking duties and he thumped the ball past Gerrard to give Liverpool a 3-1 lead 15 minutes from time.
Liverpool had chances to extend their lead in the final minutes of the game, but they were content to play out the closing moments and move into third in the table and send the red half of Merseyside home happy.
