The home side's first chance of the afternoon came when Luis Suarez clipped the outside of the post.
However, both he and the Reds didn't have long to wait for the opening goal. The Uruguayan skipped past three West Brom defenders before finding the bottom corner of the net.
Just six minutes later and Liverpool extended their lead, and again it was Suarez who did the damage. This time, Daniel Sturridge played the ball wide to Mamadou Sakho, who crossed for Suarez to head home from outside the 18-yard box.
West Brom could have pulled one back before the break, but Nicolas Anelka's effort was knocked wide by Skrtel after the ball had bounced past Simon Mignolet.
Soon after the restart Suarez grabbed his and his team's third of the afternoon, heading in Gerrard's delivery.
Sturridge then saw his effort smack the underside of the crossbar.
However, Sturridge restored the Reds' three-goal lead with a run and chip over Boaz Myhill's head.
Suarez then almost scored his fourth of the afternoon with an overhead kick that rebounded back off the bar.