Torres will dominate the headlines having notched 50 goals in 72 Premier League matches, but much of the credit should go to Pepe Reina, who kept his team in contention with a couple of magnificent saves.
He helped Liverpool to only their sixth win from 19 matches in all competitions, which lifts them above Birmingham into seventh, four points behind fourth-placed Tottenham and two adrift of Villa.
Martin O'Neill's men drop down to sixth having scored fewer goals than Manchester City and they are entitled to feel totally deflated by their last-gasp defeat.
The sense of importance surrounding the match was heightened by the knowledge that a win for either side would boost their top-four aspirations.
And there was little to choose between them during a cautious opening period that saw both teams zip the ball around with confidence and work hard for an early breakthrough.
Alberto Aquilani was handed his second start in four days at the heart of Liverpool's 4-4-1-1 formation and the Italian midfielder linked well with Gerrard and Torres.
Gerrard came close to opening the scoring when he collected a Torres pass and curled a dipping first-time strike towards goal, only for a back-tracking Brad Friedel to tip it over the bar.
For all their effort, Villa's desire to prise open the Liverpool defence was undermined by a lack of creativity in midfield.
With Ashley Young suspended, the recently impressive James Milner was deployed on the left of a 4-4-2 system and the Englishman struggled to assert his authority on proceedings.
The hosts had to wait 24 minutes for their first shot on target - Milner drove tamely at Reina - but they were gifted an opening on the half-hour.
Torres and Gerrard combined to secure Liverpool's victory
Milner hoisted a corner to the back post where a completely unmarked Downing saw a smashed volley expertly saved from point-blank range by the arm of Reina.
At the other end, Liverpool felt they should have been awarded a penalty for a mis-timed tackle by Richard Dunne on Dirk Kuyt, but referee Lee Probert waved away their appeals.
Amid bitterly cold conditions and heavy snowfall, the players deserved credit for the general quality of the first half - but the same could not be said about much of the second.
Despite Liverpool having lost four of their previous six away league games, Villa strikers Agbonlahor and Carew posed little threat to the visitors' back four.
That said, the hosts' midfield became sloppy as the match wore on, starving their front men of service and allowing Liverpool to push forward at every opportunity.
But the Anfield club could not translate their dominance into goalscoring chances and Torres looked particularly off-form.
The game was in desperate need of a goal and the breakthrough might have arrived when Agbonlahor capitalised on Jamie Carragher's slip to race clear, but his low effort was turned behind by Reina.
Moments later, Carew glanced a header just wide of the far post from Milner's corner and Villa had a penalty shout rejected when Emiliano Insua appeared to head the ball on to his arm.
When the fourth official indicated four minutes of injury time it was Villa who seemed most likely to go on and snatch a last-gasp winner.
But the hosts carelessly relinquished possession and after a ricochet put Torres clean though on goal, the 25-year-old made no mistake with a crisp finish into the bottom corner.
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