After Sunday's defeat to Tottenham, Liverpool desperately needed a victory against Stoke to prevent their title challenge being still-born, and they got it by the comfortable margin of 4-0.
'It was important to score an early goal, and that changed the game,' said Liverpool manager Rafa Benitez.
'They continued with their game plan, but we were still attacking. The second goal changed things because they had to attack, and there was more space for us.'
Torres eased Liverpool nerves after just four minutes, converting Steven Gerrard's cross from eight yards out.
An acrobatic finish from full-back Glen Johnson, after Dirk Kuyt's initial header had been saved by Thomas Sorensen, gave them a second just before half-time.
'(Johnson) was doing well,' Benitez said. 'We know that in attack he is a good player.'
Second-half goals from Kuyt and David Ngog completed an easy win.
Tottenham cruised to a second victory of the season, winning 5-1 at Hull.
Jermain Defoe latched onto a Tom Huddleston pass to give Spurs a 10th-minute lead, and Wilson Palacios drilled a second four minutes later.
Stephen Hunt's 21st-minute free-kick swooped untouched through a cluster of players and in at the far post.
Defoe beat Michael Turner and thrashed his second shortly before half-time.
Robbie Keane made absolutely sure of the points 12 minutes from time, before Defoe completed his hat-trick in injury-time.
An injury-time penalty from James McFadden earned Birmingham a 1-0 win over Portsmouth in the night's other game.