The Spain star opened the scoring in the 26th minute before Ryan Babel made it two just two minutes later.
Alberto Aquliani grabbed their third in six minutes on 32 minutes with Torres adding his second 13 minutes from time before Nadir Belhadj had the final say with a consolation in the closing moments.
Portsmouth had been comfortable enough for the opening quarter with a half-hearted penalty appeal for Ricardo Rocha's handball the only cause for concern.
Steven Gerrard also went close from the edge of the box when he should have hit the target, but Liverpool went ahead in the 26th minute.
Pompey keeper Jamie Ashdown, who was deputising for the injured David James, smashed a clearance into Gerrard and Maxi Rodriguez played in Torres to tap in his 14th of the season.
Two minutes later it was 2-0 when Torres turned provider with a cross that was stabbed home by Babel.
And the match was all over as a contest in the 32nd minute when Gerrard found Torres and he back-heeled into the path of Aquilani to fire in his first goal for the club from 12 yards.
The Reds were rampant with Gerrard somehow firing wide and Torres slamming a shot against the post.
Pompey finally responded a minute before the break with Frederic Piquionne coming within inches of converting Jamie O'Hara's cross.
Ashdown atoned for his earlier error soon after the interval with a stop form Gerrard's shot before he superbly tipped another Babel shot onto the bar.
Pepe Reina was then forced into action soon after when he clawed over Michael Brown's shot from the edge of the box.
Gerrard was lucky to stay on the pitch 17 minutes from time when he appeared to strike Brown with his arm but the win was sealed on 77 minutes.
Aquliani fed Torres and he turned past Rocha and smashed his shot beyond Ashdown.
But the visitors had the last word when Piquionne crossed for Belhadj to tap home with two minutes remaining.