Fernando Torres struck twice in three minutes as Liverpool comfortably eased past Everton in the Merseyside derby.
Torres slid home Robbie Keane's cross after 59 minutes then pounced on a loose ball to score from close range after Phil Jagielka tackled Dirk Kuyt.
Tim Cahill had Everton's best chance after 13 minutes but mis-kicked from Mikel Arteta's corner.
Everton's misery was complete when referee Mike Riley sent Cahill off for fouling Xabi Alonso after 80 minutes.
It was a victory that gives Liverpool their best start to a Premier League season - with star striker Torres ending a barren six-game sequence in style and keeper Pepe Reina not having a save to make in the match.
But Everton's struggles continue as this marked their third home defeat in three league games this season - and they now face a pivotal Uefa Cup clash with Standard Liege in Belgium on Thursday with the tie locked at 2-2.
Everton recalled Tony Hibbert for the first time this season after knee surgery, allowing Phil Neville to push into central midfield alongside £15m club record signing Marouane Fellaini.
Liverpool dominated possession for lengthy periods of the first half, but failed to test Everton keeper Tim Howard.
Everton's Cahill had the best chance after 13 minutes when Arteta's corner squirmed through to find him unmarked, but the Australian midfield man could not make proper contact when unmarked only eight yards out.
Torres was unhappy at what he clearly felt was an over-physical approach from Everton's defenders, and his frustration increased when he saw a goal-bound shot on the turn blocked by Jagielka.
The Spanish striker finally tested Howard with a tame effort after 51 minutes, and Steven Gerrard was only inches off target seconds later with an angled drive that had Howard scrambling.
Torres finally got it right after 59 minutes when he was allowed to escape at the far post to expertly steer in a perfect cross from Keane.
And he slammed in a second from close range three minutes later when he pounced after Jagielka's excellent tackle denied Kuyt right in front of goal.
He thought he had completed a five-minute hat-trick when he beat Howard again from close range, but referee Riley awarded a free-kick against Kuyt.
Everton had barely threatened the Liverpool goal, but they almost pulled one back with 13 minutes left when Joleon Lescott's cross flew across the face of goal with Fellaini and Yakubu unable to apply the finishing touch.
And Everton's miserable afternoon got worse a minute later when Cahill was shown the red card by Riley for a foul on Alonso.
Everton substitute Louis Saha shot just wide with seconds remaining - but it was a minor inconvenience to Liverpool keeper Reina on what was otherwise an afternoon of dominance for Rafael Benitez's side.
Everton: Howard, Hibbert (Saha 63), Yobo, Jagielka, Lescott, Arteta, Neville, Fellaini, Osman, Cahill, Yakubu.Subs Not Used: Nash, Baines, Castillo, Vaughan, Nuno Valente, Rodwell.
Sent Off: Cahill (80).
Booked: Fellaini, Yakubu, Neville.
Liverpool: Reina, Arbeloa, Carragher, Skrtel, Dossena, Kuyt, Alonso (Leiva Lucas 86), Gerrard, Riera (Aurelio 67), Torres, Keane (Pennant 86).Subs Not Used: Cavalieri, Hyypia, Agger, Babel.
Booked: Alonso, Torres, Arbeloa.
Goals: Torres 59, 62.
Ref: Mike Riley (Yorkshire).