With only six games of the season remaining, the momentum is with the Reds as they cruised to their sixth win in seven Premier League matches, while David Moyes' side have taken only one point from their last three encounters following a defeat at Fulham and draw with West Ham United.
After a week of controversy following Javier Mascherano's red card in the 3-0 defeat at Manchester United, Liverpool boss Rafa Beinitez opted for experience with John Arne Riise and Sami Hyypia coming in for Alvaro Arbeloa and Fabio Aurelio.
He also decided to replace the suspended Mascherano with Lucas Leiva while Everton brought back Steven Pienaar and Joseph Yobo for Leighton Baines and the injured Tim Cahill, who will not play again this season.
Andrew Johnson missed out because of a groin problem so Yakubu was forced to plough a lone furrow up front.
It was a mistake by the Nigeria international that led to the only goal of the match. He lost control of the ball close to his own penalty area in the seventh minute allowing Torres to mark his first derby game with a goal.
The ball fell to the in-form Spaniard who was able to turn and fire a first-time shot past the despairing dive of Tim Howard.
From that moment on the first half was one-way traffic as Liverpool threatened to run riot. In the 16th minute Howard was forced to tip Dirk Kuyt's drive away for a corner after the Dutchman had been expertly set up by Torres.
Just 12 minutes later Riise's powerful run and cross from the left should have been turned in by Ryan Babel who seemed undecided whether to go for the ball with his head or foot and the chance was lost.
After 32 minutes Lee Carsley did well to win the race to get to Steven Gerrard's free-kick ahead of Lucas as he powered a header over his own bar, and five minutes before the interval a stunning 30-yard Gerrard volley beat Howard only to come back off the post as the Reds continued to dominate proceedings.
Everton improved after the interval and Leon Osman glanced a header narrowly wide just after the hour mark, the first clear opening the visitors had created.
Yakubu should have been booked for an outrageous dive inside the penalty area almost immediately afterwards but Liverpool continued to look assured at the back.
Benitez's side only looked like adding to their tally after the break in the closing stages when Kuyt's shot was deflected narrowly wide and Howard was forced to make a fine save to deny Gerrard's thunderbolt.
But they successfully snuffed out any potential raids by the visitors, whose season is in danger of petering out, to clinch three vital points.