The Spain striker struck in the third minute and again on the hour after Glen Johnson had scored Liverpool's second.
"My goals are because the team is playing really well," Torres said. "Hopefully the best goals are to come. We have six games to play and we have to keep playing like this." The victory moved Liverpool up to fifth in the Premier League, four points behind fourth-place Tottenham having played a game more.
At the wrong end of the standings, Burnley's hopes of surviving the drop were hit by a 1-0 home loss to Blackburn in Sunday's other match.
For Liverpool, an eighth straight victory at Anfield never looked in doubt after a high-tempo start saw Torres score in the opening minutes for the second successive Sunday.
Goalkeeper Pepe Reina's long kick reached Torres on the left flank and the striker dribbled his way inside Michael Turner before curling a shot over Craig Gordon into the far top corner.
Liverpool was passing the ball around sharply and incisively, but took until the 32nd minute to go further in front.
Captain Steven Gerrard's in swinging corner was only cleared to the edge of the penalty area and Glen Johnson touched the ball inside on to his left-foot and unleashed a shot which took a deflection off Turner to beat Gordon.
As Liverpool continued to overwhelm Sunderland after the break, Johnson set up the third by threading the ball through to Torres, who spun on the penalty spot before nudging it past Gordon.
"We now have confidence that we can beat anyone and we must beat everyone until the end of the season," Torres said.
At Turf Moor, Burnley saw its hopes of a second successive season in the top flight - after a 33-year absence - slip further away.
Losing to local rival Blackburn keeps Burnley three points from safety with six matches to avoid relegation.
Blackburn's winner came from David Dunn's 20th-minute penalty kick after Burnley goalkeeper Brian Jensen was adjudged to have tripped Martin Olsson.
Replays suggested Olsson was already going to ground before any contact was made.
"When you look at it in the cool light of day it's clear it's not even a penalty," Burnley manager Brian Laws said.
"Olsson's took a dive, he's conned the referee. The referee's not in a great position and he's given the penalty which was very harsh and left us with a mountain to climb." Sam Allardyce acknowledged that his Blackburn side had been fortunate to be awarded the penalty that led to Rovers moving up to 10th in the standings.
"It's slightly harsh against Burnley when you look at it from the angles and you slow it down," Allardyce said.
"But when you look at it from Mike Dean's position and his point of view it definitely looks like a penalty." Manchester United tops the standings after beating Bolton 4-0 on Saturday to remain a point ahead of Chelsea, which routed Aston Villa 7-1.
