Everton 0-3 Liverpool
Liverpool put Merseyside neighbours Everton in their place with style to record a comfortable first victory of the season at Goodison Park.
Michael Owen struck twice either side of half-time to put Gerard Houllier's side in the driving seat - and Harry Kewell added to the red celebrations with his first goal for the club late on.
Owen's double and Kewell's late strike gave Liverpool their first goals from open play this season - and relieved the pressure on Houllier after a barren start to the Premiership campaign.
But it was a day of misery for Everton, who saw a week of frustration in the transfer market worsened by a fourth straight Goodison defeat against their arch-rivals.
Everton suffered a blow prior to kick-off when goalkeeper Richard Wright was ruled out with a knee injury, being replaced by Steve Simonsen.
Liverpool were without Stephane Henchoz, with Igor Biscan continuing in central defence alongside Sami Hyypia.
Everton's ploy was to release the pace of Wayne Rooney and Tomasz Radzinski - with the latter an early threat.
38 mins: Owen puts Liverpool ahead
51 mins: Owen doubles Liverpool's lead with a cool finish
79 mins: Kewell's shot wraps up Liverpool's win
Radzinski raced on to Rooney's pass but fired across the face of goal.
And it took a brilliant saving tackle from Biscan to halt Radzinski as he looked to take advantage of another Rooney through ball.
Liverpool took time to settle, but their passing game exerted a measure of control and they went ahead seven minutes before the interval.
Kewell stabbed a pass through to Owen, who took advantage of hesitation from Alesssandro Pistone to beat Simonsen.
Everton had an instant chance to restore equality when Rooney took a return pass from Steve Watson, but he failed to control and Jerzy Dudek made a smothering save.
Liverpool responded with a trademark counter attack and it took a fingertip save from Simonsen to deny Kewell his first Liverpool goal.
Everton made a change at the interval, sending on Thomas Gravesen for the struggling David Unsworth.
And Moyes' side were almost level within seconds of the re-start when Dudek fumbled Mark Pembridge's free-kick and Liverpool survived a scramble.
But Liverpool delivered a hammer blow after 51 minutes when Milan Baros shrugged off weak defending from Joseph Yobo to set up Owen to score from 10 yards.
Dudek was having an eventful game and he produced a stunning reflex save to stop Rooney's header from Gravesen's corner.
Everton made a substitution with 20 minutes left, sending on Duncan Ferguson for Tobias Linderoth.
And the big Scot almost threw Everton a lifeline with 12 minutes left, sending a free-kick against the underside of the bar from 20 yards.
Liverpool wrapped up victory with eight minutes left, with Kewell opening his goal account.
Everton goalkeeper Simonsen was at fault, racing from goal but failing to get the ball, allowing Owen to cross for Kewell to score.
Everton: Simonsen, Pistone, Yobo, Stubbs,
Unsworth (Gravesen 45), Watson, Linderoth (Ferguson 71),
Pembridge, Naysmith, Radzinski, Rooney.
Subs Not Used: Weir, Chadwick, Turner.
Booked: Naysmith, Watson, Rooney.
Liverpool: Dudek, Finnan, Biscan, Hyypia, Carragher, Gerrard,
Diouf (Riise 89), Smicer (Murphy 72), Kewell,
Baros (Heskey 73), Owen.
Subs Not Used: Diao, Kirkland.
Booked: Kewell, Finnan, Baros.
Referee: M Riley (W Yorkshire).