Captain Steven Gerrard's ninth-minute penalty gave them the ideal start in the last 16 clash at Anfield, after Lucas Leiva had been fouled.
Torres then struck twice in the second half - his first European goals for more than 11 months - to put his side into the quarter-finals.
Trailing 1-0 from the first leg an early Liverpool goal was essential to ease the pressure and, watched by Argentina coach Diego Maradona, they produced just that.
The much-maligned Lucas, returning to the side because of Alberto Aquilani's illness, dribbled into the area and produced a tidy piece of skill to go past Adil Rami and draw the foul.
Referee Nicola Rizzoli pointed to the spot and Gerrard confidently fired home to level things up on aggregate.
Torres had two half-chances to double the lead in the next five minutes as first he cut in from the right at pace only to see his near-post shot deflected wide before then lofting a shot over from Javier Mascherano's free-kick.
Despite going behind Lille still looked like they could be a danger on the counter-attack with Eden Hazard, goalscorer a week ago, and Ludovic Obraniak posing a threat from the flanks.
But right-back Glen Johnson was getting forward at every opportunity and when he found himself in the penalty area he hit a left-foot volley straight at goalkeeper Mickael Landreau.
Daniel Agger's glancing header from Gerrard's inswinging 31st-minute corner was eventually stopped by Landreau on the goalline after the ball got stuck between Dirk Kuyt and Franck Beria.
Lucas, having his best spell for some time, then shot straight at the goalkeeper from 20 yards.
A minute later Hazard burst past Agger and Johnson into the area and had only Jose Reina to beat but the goalkeeper stood tall and the shot deflected behind off his head.
Five minutes before half-time Torres headed Kuyt's hanging cross back across goal but wide of the post.
Lille came out after the break with more purpose and Jamie Carragher produced a perfectly-timed tackle to deny Rio Mavuba three minutes into the second half.
But a minute later Liverpool seized control of the tie with an expert piece of finishing from Torres.
Ryan Babel hooked a ball out of defence with his right foot which looked more like a clearance than a pass but Rami, who had been given a torrid time by Torres, misjudged the bounce of the ball and it ballooned over him.
The Spain striker did not need a second invitation and he sped towards goal before dinking a shot past Landreau with the outside of his right foot.
It was the first time he had scored in European competition since his goal at Anfield in the 3-1 Champions League quarter-final defeat to Chelsea on April 8.
Torres then drilled a shot just wide of the goalkeeper's right-hand post.
Liverpool's advantage was only a slender one and that fragility was almost exposed in the 73rd minute when Obraniak's free-kick picked out Pierre-Emerick Aubameyang at the far post only for the substitute to bundle his shot into the ground and over the crossbar.
As the tie entered its final throes the anxiety began to grow as Liverpool were unsure whether to try to hold their lead or finish Lille off with a third goal.
It almost came when Kuyt's long-range strike was batted behind by Landreau.
But all the pressure was released when Torres followed up a rebound from Gerrard's shot to score his second a minute before time and his fourth in his last two .
It secured a second victory in an important week, with Manchester United to come at Old Trafford on Sunday.
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