A brace apiece from Xabi Alonso and Fernando Torres and goals from Ryan Babel and Andriy Voronin swept the Rams aside as Rafa Benitez's men showed they mean business in the Premier League this season.
The Reds started brightly and came close to scoring within three minutes when
Danish defender Daniel Agger's deflected shot was tipped round the post by goalkeeper Stephen Bywater.
And minutes later the Derby keeper had to be at his athletic best to save a thunderous Torres header after smart wing play from Jermaine Pennant.
But it was Benitez's men who looked the more threatening and on 15 minutes came close again through Dirk Kuyt.
The breakthrough was only a matter of time and it came from Spanish free-kick specialist Xabi Alonso, the midfielder curling a 35-yard cross-cum-shot that sailed past Bywater's despairing dive.
The rampant Reds were cutting hapless Derby apart and they made it 2-0 on the stroke of half-time with an exquisite move.
Agger fed full-back Alvaro Arbeloa with a defence-splitting pass and the Spaniard found debutant Babel who turned and buried his shot in the corner of the net.
After the break, Liverpool continued where they left off and should have tripled their lead with a sweeping move but Xabi Alonso blazed over.
But Torres made it three on 56 minutes turning the Derby defence inside out before sliding the ball past Bywater.
A tide of Red attacks followed and Alonso made it four after 68 minutes when he picked up a loose ball on the edge of the box and coolly slotted home.
Substitute Voronin then joined in the party latching onto a shot from Kuyt to smash in the fifth.
Torres rounded the keeper to score his second and Liverpool's sixth after Derby sorry defence left him through on goal.