With Arsenal extending the gap to 13 points ahead of Liverpool, the home team had to win to have any chance of staying in touch with the league leaders.
The Reds flew out of the box from the opening whistle and set about taking apart a very defensively-minded Pompey side.
The first opportunity of the game came in the tenth minute as Torres set about his business, easily outpacing Sylvain Distin in the box and unselfishly laying the ball to his strike partner Dirk Kuyt.
The Dutchman looked almost certain to score before a well-timed sliding tackle by right-back Glen Johnson took away the chance.
With the home team dictating the pace it was only a matter of time before the deadlock was broken and the Reds' first goal came in the 13th minute with a superb right-foot volley from Yossi Benayoun.
After a surging Torres run into the box a well-timed tackle by Distin placed the ball at the feet of Aussie winger Harry Kewell, whose pin-point cross saw Benayoun hammer home his sixth goal of the season.
The visitors were subject to wave after wave of Liverpool pressure and the home team saw their lead doubled three minutes later through an unlucky own goal by Distin.
An intercepted ball on the halfway line released Kuyt down the right who played into Torres' feet inside the box, but a tackle by Sol Campbell saw the ball hit Distin's knee and fly past a stranded David James.
Even with the middle of the park packed with blue shirts, the visitors still could not deal with the passing and movement of the home side and with only Benjani upfront, the visitors never really troubled the Liverpool backline.
Two changes made by Harry Redknapp at half-time saw the Pompey side change from a 4-5-1 to a more attacking 4-3-3 and the visitors came out all guns blazing.
The replacment of winger John Utaka with the lanky striker Nwankwo Kanu looked a stroke of Redknapp genius as the visitors pulled one back just ten minutes into the second half.
A ball played into the feet of the Nigerian was easily controlled and a good turn and cross found Benjani, whose piece of fancy footwork shifted the ball from his right to left, before he drilled it past a stationary Jose Reina.
In total contrast to the first half, the visitors looked a different team and started to get a foothold back in the game, but the Reds once again showed their class as £25million Torres restored the two-goal cushion with an easy sidefooted finish.
A 30-yard pass from the Javier Mascherano found Ryan Babel inside the box and an on-rushing James could only block the ball with his body, sending it straight to the Spaniard who calmly placed it in the bottom corner.
The game was put well out of Portsmouth's reach when the home side made it 4-1 through a sublime left-foot volley by man-of-the-match Torres.
A ball into the box by Jamie Carragher found Liverpool captain Steven Gerrard's head and a little nod down was perfect for the Spaniard to smash home his second of the game.