Liverpool steadied their early nerves with a comfortable win that left West Brom awaiting their first league win.
Steven Gerrard rounded off a slick move to open the scoring and a cool-headed Steve Finnan effort put Liverpool comfortably ahead at the break.
West Brom became more involved after the break but when Luis Garcia hammered home a third, following up his own blocked shot, the points were safe.
Robert Earnshaw came on for his West Brom debut but made little impact.
West Brom's Martin Albrechtsen had already nearly put through his own net before Gerrard rewarded Liverpool's early pressure with the first goal.
He combined with Garcia and Finnan to charge through on goal and kept his balance to shoot home from close range.
That lead was nearly extended when Neil Clement's attempted clearance was cleared off his own line, and from the resulting corner Sami Hyypia went close with a header.
Clement's off-target header from a Jason Koumas corner was West Brom's first meaningful effort on goal before Garcia wasted a glorious chance to double Liverpool's lead when his free header was way off target.
Finnan claimed his first league goal for Liverpool to make it 2-0 when he trapped Jon Arne Riise's cross-field ball superbly and slotted home from a tight angle.
Clement again went close for Albion in the dying seconds of the half but Djibril Cisse nearly made it 3-0 as Liverpool went in comfortably ahead at the break.
Earnshaw came on just after half time as the visitors began to get more involved in the game, before Garcia wrapped up the points when he followed up his own blocked shot to thump home.
Koumas soon tested Jerzy Dudek with a low long-range effort but with Liverpool showing no likelihood of letting their lead slip, the game was over as a serious contest.
Near the end, substitute Milan Baros had strong penalty appeals waved away when West Brom captain Darren Purse brought him down on the edge of the box.
And keeper Russell Hoult needed to be at his best to block Cisse's late effort as Liverpool eased to victory.
Liverpool: Dudek, Josemi, Carragher, Hyypia, Riise, Finnan, Hamann, Gerrard (Alonso 65), Kewell (Baros 68), Cisse, Luis Garcia (Traore 74). Subs Not Used: Diao, Luzi Bernardi.
Goals: Gerrard 16, Finnan 42, Luis Garcia 60.
West Brom: Hoult, Scimeca, Purse, Albrechtsen, Robinson, Haas (Gera 66), Koumas, Clement, Greening,
Horsfield (Earnshaw 53), Kanu. Subs Not Used: Kuszczak, Dobie, Contra.
Ref: S Dunn (Gloucestershire).