Steven Gerrard's dipping free-kick ensured Liverpool secured a narrow win.
Torres had an encouraging debut for Liverpool
Liverpool took a first-half lead with a helping hand from Villa through Martin Laursen's own goal after Stuart Taylor pushed away Fernando Torres' shot.
The visitors missed a catalogue of chances and with five minutes left Gareth Barry's penalty pulled Villa level after Jamie Carragher's handball.
But Gerrard had the last word - as he has so often - arcing the ball over the Villa wall into the roof of the net.
Carragher's indiscretion had looked like it was going to cost Liverpool two points as the visitors failed to build on their first-half lead.
Before scoring, Gerrard had gone close with a couple of shots, while substitute Ryan Babel went also close with two efforts.
If manager Rafael Benitez will be hoping his side become more adept at killing games off, he will have been encouraged by Torres' debut.
Of the host of players Benitez splashed out £45m on during the summer only Torres was deemed worthy of a place in Liverpool's starting line-up.
The former Atletico Madrid striker showed some intelligent forward play and struck up a good understanding with Dirk Kuyt.
It was the Dutchman's dummy that allowed Gerrard's pass to run through to Torres in the build-up to the first goal.
Taylor managed to get a hand to Torres' shot, but Kuyt was quick to reach the ball before it went out for a corner and his cross was stubbed into the net by the luckless Laursen, who was sustituted at the interval.
While Benitez has spent lavishly, Martin O'Neill has adopted an altogether more frugal approach - so far - to the transfer market and on the evidence of this 90 minutes Villa could do with some fresh blood.
Craig Gardner forced a save from Jose Reina with a rising shot early on, while Carragher also needed to be alert to block an effort from John Carew.
Villa rallied at the conclusion of the first-half, Stilian Petrov shooting straight at Reina, while Young should have done better when the Liverpool goalkeeper failed to hold a cross from the left.
After Gardner threw himself at the ball to block a Gerrard shot, the Liverpool captain, who was playing in the centre of midfield, drew a fine save from Taylor following another Liverpool counterattack.
With 15 minutes left Ryan Babel made his Liverpool debut, immediately going close when he lashed a shot wide.
Babel's cameo appearance was also impressive, the Dutchman firing in another shot that required Taylor to push the ball away.
With five minutes remaining Villa found themselves level when Barry calmly stroked the penalty home after Carragher's handball.
It was unfortunate for Carragher, who had marshalled the Liverpool defence very effectively for the previous 84 minutes.
But Villa were to be level only momentarily as Gerrard's brilliance secured Liverpool all three points.
Aston Villa manager Martin O'Neill:
"We got ourselves back in the game after they took the lead.
"We tried to play strongly against a very fine side, but didn't quite have real self belief. I think I have more belief in the team than they have.
"We're a young side. We're in the throes of building a team, but we don't want to take too long about it."
Liverpool manager Rafael Benitez:
"The team deserved to win.
"We were really good. For me there were two or three positive things but due to their keeper we couldn't score."
"Steven Gerrard's winning goal was fantastic. It was the right final score for us."
Aston Villa: Taylor, Gardner, Mellberg, Laursen (Cahill 46), Bouma (Moore 71), Petrov, Reo-Coker, Barry, Agbonlahor, Carew, Young.
Subs Not Used: Harewood, Osbourne, Maloney.
Booked: Mellberg, Bouma, Barry, Petrov.
Goals: Barry 85 pen.
Liverpool: Reina, Finnan, Carragher, Agger, Arbeloa, Pennant (Babel 74), Gerrard, Alonso, Riise, Torres (Voronin 79), Kuyt (Sissoko 90).
Subs Not Used: Itandje, Hyypia.
Booked: Pennant, Reina.
Goals: Laursen 31 og, Gerrard 87.
Ref: Mike Riley (England).