Liverpool made it 10 home goals in a week to underline the belief at Anfield that they are genuine Premier League title contenders.
They followed up the four they put past Toulouse in the Champions League on Tuesday with six unanswered goals to crush Derby.
Spaniards Fernando Torres and Xabi Alonso grabbed two each, Ryan Babel netted his first for the club and substitute Andriy Voronin also got onto the scoresheet.
It is the first time Liverpool have led the top flight for five years and their best start to a league season since 1998.
You had to feel sorry for Derby. Fresh up from the Championship, they simply could not cope with the variety, pace and skill Liverpool possessed - or indeed the pots of money that has seen boss Rafael Benitez build his squad.
Benitez made five changes from the side that beat Toulouse in midweek, with Peter Crouch not even on the bench and Dirk Kuyt and Torres being paired up front.
Derby duo Claude Davis and Tyrone Mears both passed fitness tests for the Premier League's bottom club, but Dean Leacock missed out with a toe problem.
Steven Gerrard and Jamie Carragher watched from the directors' box, as both were still injured for Liverpool, who recalled Steve Finnan, Alonso, Jermaine Pennant and Babel along with Torres.
Without Paco Ayestaran - his assistant for 11 years at three clubs - alongside him, Benitez watched his team start with confidence and cruise through the game.
Ayestaran has shocked the Liverpool backroom by deciding he wants to leave, after what is believed to be several recent differences with Benitez.
How this affects the smooth running of Liverpool long term remains to be seen, but the players set about finding the gaps in Derby's rearguard with single-minded determination.
Daniel Agger saw a 25-yard shot clip Bob Malcolm and force Stephen Bywater into a flying save. The goalkeeper was in action again when he fielded Torres' header powered in from Pennant's cross.
Mears ventured forward to blast a 20-yard shot over the bar, and Stephen Pearson wasted possession after robbing Javier Mascherano and chasing 40 yards before a poor pass let Liverpool off the hook.
But that was about it from Derby in the first period as they became increasingly occupied by the Red tide coming their way.
Kuyt cracked a 25-yard shot just over the angle and Mascherano saw a long-range effort skim the far post.
Derby were battling hard, trying to restrict the space in front of their defence, but it was becoming increasingly difficult and Mears was warned by referee Alan Wiley for a succession of fouls.
After one on Pennant, Alonso took the free-kick 35 yards out on the left. As his low drive swerved into the box Kuyt ran across Bywater's line of vision and the ball nestled in the back of the net.
Kuyt should have made it two when Pennant raced away on the left to lift in a cross for the unmarked Dutchman to head over from eight yards.
Two minutes later Pennant's pace and skill severely embarrassed Malcolm and, from yet another cross, Kuyt was there again to lift his effort over the bar.
Liverpool were pouring forward now, and after one sustained run from Finnan, the cross was controlled superbly by Torres before the striker cracked his effort over the top.
Derby were praying now to get to the break without further damage but they were to be disappointed. The second goal came in first-half injury-time when Pennant set up Babel, who side-stepped two diving defenders before belting in his first goal for the club.
The second period started just as ominously for Derby. Pennant, Torres and Kuyt combined to set up Alonso from 10 yards, but the Spaniard lifted his effort into the Kop.
The third was not long coming. Mascherano dispossessed a dithering Malcolm 30 yards out and pushed the ball to Torres. The Spaniard then took on a beat three defenders in a run across the box before burying his shot into the bottom corner on 56 minutes.
Three minutes later the hapless Malcolm was withdrawn to save him further punishment, and Gary Teale came on.
Liverpool were playing at such a pace and with outstanding control, Derby just could not handle it and continually gave the ball away or made forced errors.
Liverpool's response was to take off the excellent Pennant, to a rousing ovation, with Yossi Benayoun coming on. Derby then took off Mohammed Camara - another defender out of his depth - and replaced him with James McEveley.
Andy Griffin was booked for pulling back Torres on 65 minutes, with the Liverpool attacks incessant. The fourth came on 69 minutes when Babel crossed from the right, Benayoun's effort was blocked and Alonso placed an 18-yard shot into the bottom corner.
Next on was Andriy Voronin in place of Babel and virtually his first touch produced the fifth. Kuyt surged into the box on the right and fired in an angled shot that Bywater could only push out for the Ukrainian to force home from a couple of yards.
It got worse for Derby a minute later when a poor back-pass by Andy Todd was snapped up by Torres, who rounded Bywater to run the ball into an empty net.
Mohamed Sissoko came on for Mascherano between the fifth and sixth goals, Darren Moore being sent on by Derby for Griffin on 80 minutes, and Derby survived without any further damage.
