Preston had the first chance after five minutes when captain Paul McKenna was fouled and Ross Wallace - who is on loan from Sunderland - hit a 25-yard free-kick which Liverpool keeper Diego Cavalieri turned away for a corner.
Steven Gerrard replied for Liverpool with a 20-yard shot which was saved and Preston central midfielder Richard Chaplow had a 20-yard effort similarly repelled.
Ex-Liverpool striker Neil Mellor got down the left wing and cut inside Sami Hyypia and hit a 20-yard right foot shot which was saved.
Liverpool made it 1-0 in the 25th minute when Chaplow didn't clear the ball, Xabi Alonso crossed with the assist and Albert Riera on the right-hand byline cut inside before hitting a stunning left-foot shot high into the net from an impossible angle.
Chaplow was the only booking of the game after 34 minutes for a foul on Alonso and it was the Spaniard who had a shot saved just before half-time after Robbie Keane had a left-foot effort turned away.
Liverpool's man of the match Gerrard forced two good saves out of Preston keeper Andy Lonergan.
On the hour-mark a 25-yard lob and then a 20-yard shot which was tipped over for a corner.
If Jon Parkin hadn't have pulled back Jamie Carragher, Preston might have equalised on 64 minutes when a Chaplow cross was headed home by Sean St Ledger but this was disallowed for the foul.
Carragher fouled Wallace on the left and McKenna hit a free-kick across goal which hit St Ledger on the leg from close range and was saved.
Late in the game, Gerrard had another 20-yard shot which was saved and then, in the third minute of added time, a long ball by Carragher found Gerrard and he ran through before squaring the ball unselfishly to substitute Fernando Torres and he scored from three yards to finish the game.