كتب : Hatem Maher
The Reds dominated the entire match and found no difficulty in opening the scoring after 26 minutes.
Alonso intended to curl in a free-kick but his ball surprisingly went into the back of the net after Derby keeper Stephen Bywater lost ball sight due to Dirk Kuyt's run in front of him.
Dutch winger Ryan Babel scored his first goal for Liverpool just before the break to double the lead following a skilful move.
He collected Alvaro Arbeloa's pullback, sidestepped two defenders and buried home past Bywater.
Torres killed off Derby hopes 11 minutes after re-start when he slotted into the bottom corner of the net after being set-up by Javier Mascherano.
Alonso made it four nine minutes past the hour mark after hitting a low shot from the edge of the area into the net.
In the 76th minute, Ukrainian striker Andriy Voronin scored on the rebound before Torres completed the rout one minute later when he capitalized on a defensive blunder to round Bywater and slot home.
Liverpool are in charge of the Premiership table with 10 points while Derby lie at the bottom on just one point as they are yet to grab a win.
Elsewhere, Middlesbrough continued their recent fine form with a 2-0 home victory over Birmingham City.
David Wheater broke the deadlock in the 12th minute before Stuart Downing ensured the win eight minutes before the break.
Egyptian striker Mido took part in the game and put in a fine display. He was replaced by Lee Dong-gook four minutes from time.
Michael Owen's strike was enough to give Newcastle United a 1-0 victory over 10-man Wigan.
The England striker cut ahead of the keeper to head home Obafemi Martins cross at the near post.
Wigan played most of the second-half with men on the field after Kevin Kilbane was sent off for a second bookable offense.