Hamburg SV's Mladen Petric scored with one of the best strikes of the season, volleying home from 15 meters with his back to goal, to help them win 3-1 at Standard Liege and set up a semi-final with Fulham who beat VfL Wolfsburg 1-0 away.
Petric also headed the first goal while Peru forward Paolo Guerrero, banned for the rest of the Bundesliga season for throwing a plastic bottle at a fan on Sunday, added the third - his first strike since a cruciate ligament injury in September.
Atletico Madrid grabbed their place in the last four on away goals after a stormy 0-0 draw at home to fellow Spaniards Valencia, who surrounded the referee to protest at the end after a late penalty appeal was turned down. The first leg was 2-2.
Fulham striker Bobby Zamora scored after 21 seconds as the London side, playing their 16th match of a campaign which began in Lithuania last July, continued their surprise run with a win at German champions Wolfsburg, going through 3-1 on aggregate.
Unfancied Fulham's surprise run has now taken them into the semi-finals of a European competition for the first time.
Three-times UEFA Cup winners Liverpool, trailing 2-1 from the first leg, turned their tie around in a seven-minute first-half spell with goals by Dutchman Dirk Kuyt and Brazilian midfielder Lucas lighting up the noisy Anfield crowd.
TORRES EXCITED Torres opened his account just before the hour, finishing off a counter-attack after receiving a low cross from Kuyt, and completed the scoring after being sent clear by Javier Mascherano eight minutes from time.
In between Torres' goals, World Cup-bound Paraguay striker Oscar Cardozo - who had converted two penalties in the first leg - pulled one back with a deflected free kick for his 10th goal of the competition.
"I think he (Torres) will be excited (about playing Atletico)," said Liverpool manager Rafael Benitez. "The third goal was really good. All the players had ambition to score the goal, it was crucial." Hamburg, who will host the final, completed a 5-2 win over their Belgian opponents with a Petric-inspired win.
The Croatia forward headed home from Ze Roberto's cross after 20 minutes but Igor de Camargo took advantage of hesitant defending to head in from Sebastien Pocognoli's deep free kick 13 minutes later.
It took only two minutes for Petric to strike again, this time in style.
Dennis Aogo sent over an outswinging cross from near the corner flag and Petric, marked by two defenders, produced an overhead kick to volley into the bottom left-hand corner.
Substitute Guerrero, who was also fined by his club for Sunday's incident after the goalless draw against Hanover 96, wriggled his way past two defenders and rolled the ball in off the post deep into stoppage time for the third.
STRIKER CLASH The all-Spanish tie featured a clash of two strikers heading for the World Cup, Uruguay's Diego Forlan for Atletico and Spain's David Villa of Valencia, although both drew a blank.
Forlan came close in the 48th when he raced clear and tried to emulate Lionel Messi's third goal for Barcelona against Arsenal in the Champions League on Tuesday by scooping the ball over goalkeeper Cesar Sanchez, but his effort drifted just wide.
Forlan saw another effort tipped onto the post by Sanchez in the 75th, Villa smashed a shot against the bar in the 81st and Atletico keeper David De Gea produced a stunning reaction stop from a Nikola Zigic header in the 84th.
Zigic appeared to be dragged to the ground in the penalty area by Juanito shortly after but the referee waved away Valencia's appeals and then sent coach Unai Emery to the stands for his frantic protests.
Atletico hung on for five minutes of fraught added time and furious Valencia players surrounded match officials to protest at the end.
Fulham, 2-1 ahead from the first leg, needed just a few seconds to increase their aggregate lead when Zamora scored with a deft turn and finish from a Zoltan Gera pass, his seventh goal of the campaign including the qualifying rounds.
The semi-final first legs will take place on April 22 with the second legs scheduled for April 29.
