A flat game was heading for a goalless draw until ragged Villa defending allowed the ball to slip into Torres's path and he calmly placed a low shot beyond Brad Friedel.
The Spaniard's predatory finish was his 50th league goal in 72 matches - the quickest a Liverpool player has reached that tally - and was the only memorable moment from a poor game.
The win lifts Liverpool into seventh place on 33 points - one place and two points behind Villa.
Chelsea top the standings with 45 points from 20 games. Manchester United, who host Wigan Athletic on Wednesday, are second on 40 from 19 with Arsenal third on 38 from 18 ahead of their game at Portsmouth, also on Wednesday.
Villa and Liverpool, their players perhaps chilled by relentless snow, were below par in a low-key contest.
Villa, having beaten Liverpool, Chelsea and Manchester United this season, were denied a big four clean sweep by Sunday's 3-0 loss at Arsenal and that perhaps had a chastening effect as they were cautious from the start on Tuesday.
TERRIFIC REFLEXES
Liverpool, whose away form has been poor this season, were the more aggressive side and Villa needed a good save by Friedel to keep out a Steven Gerrard shot after 17 minutes.
Liverpool keeper Pepe Reina did even better to block a fierce volley by Stewart Downing with terrific reflexes soon after while Villa forward Gabriel Agbonlahor shot straight at Reina midway through the second half.
That was about it in terms of goal threat until Torres, who had barely touched the ball all night, made the difference with a clinical finish from inside the area.
"Everyone knows when he's on form he's the best in the world, we want him to score many more goals like that and drive us into the top four," Liverpool captain Gerrard told Sky Sports.
"We're hoping this gives us a big boost. Villa, Spurs and Man City are going to keep fighting all the way and we need to do the same.
"It's important to build on this. We've virtually got everyone back fit now so there are no excuses. We need to go on a run of winning games."
Villa manager Martin O'Neill said: "We should have won but not only did we not, we lost. "We had the chances, it's a blow to the team but we will fight back."
In Tuesday's other game, Hull City fought back from two goals down at Bolton Wanderers to force a 2-2 draw thanks to a Stephen Hunt double but both teams remain in the drop zone.
