Inter, who had centre back Marco Materazzi harshly dismissed in the first leg, also went down to 10 men in the return match when defender Nicolas Burdisso was sent off for a second booking after a clumsy 50th-minute tackle on Lucas Leiva. Torres scored his fourth goal of the Champions League campaign 13 minutes later with a turn-and-shot on the edge of the area following a good run and pass from Fabio Aurelio.
The Serie A leaders had several chances at a cacophonous San Siro but Argentine Julio Cruz and strike partner Zlatan Ibrahimovic were wasteful in front of goal.
Liverpool join the other three English entrants, Manchester United, Arsenal and Chelsea, in the quarter-finals with AS Roma the only Italian side through.
"Up to the sending off it was a difficult game. I think we controlled the game and deserved to go through to the last eight," Liverpool captain Steven Gerrard told Sky television.
"I think if you look at our form over the season we are a force in Europe. We're lucky to have Fernando. He only needs one chance, as he showed tonight."
Premier League leaders Arsenal beat holders AC Milan 2-0 at the San Siro last week to win 2-0 on aggregate and although Liverpool were not as stylish they completed the job just as effectively in a fast-paced encounter.
An early long-range effort from Cruz was well saved by Pepe Reina before the Argentine shot wide after being beautifully played in by Ibrahimovic.
Swede Ibrahimovic also blasted over two free kicks and missed an excellent opportunity after an error by centre back Martin Skrtel.
Five-times European champions Liverpool were not content to sit back and made several forays forward.
Aurelio's long ball sent Ryan Babel clean through in the first period but home keeper Julio Cesar raced out of his box to clear.
Esteban Cambiasso, one of several players to lose their footing, slipped in the area and let in Torres but the in-form Spaniard shot at the keeper.
He made no mistake midway through the second half though, sending Liverpool fans wild with delight.
The Italian champions hoped to repeat their 1965 European Cup semi-final comeback when they lost 3-1 at Liverpool before winning 3-0 at home in the second leg on their way to lifting the trophy.
But Roberto Mancini's men have flattered to deceive again in the Champions League, having been dumped out by Valencia in last season's first knockout round.