Suarez completed his hat-trick early in the second half when he headed in a Steven Gerrard free-kick for the first goal to be scored in front of the Kop in the league since Suarez himself equalised in the 90th minute against Chelsea back in April.
Daniel Sturridge scored the fourth goal with a sublime chip from the edge of the area over Baggies keeper Boaz Myhill for his tenth goal of the season.
After the match, Liverpool boss Brendan Rodgers was jublulant with the form of his front two.
He told the club’s official website, “I think the front two were brilliant. Suarez’s goals were exceptional. He really exploited the space in front of their centre-halves.
“[For his first] he showed wonderful invention and creativity to nutmeg Olsson and then he took his shot really early.
“The second was a good team goal. We moved it well, the cross came in early and he guided the header in fantastically well. Then his third goal was from a great ball by Steven.
“He could have had more; he hit the crossbar and had some other opportunities in and around the area.
“I think it was his first hat-trick here at Anfield and you saw his commitment to the team and what we’re trying to do. It was a wonderful performance.”
The treble was Suarez’s fourth hat-trick for the club, his first at Anfield.