Goals from Kevin Mirallas and Morgan Schneiderlin at the end of the first half put the Toffees in control against their top-half rivals before Romelu Lukaku sealed the win late on as Everton extended their 100% home record in 2017.
The match got off to a scrappy start as West Brom looked to prevent Everton from settling into a rhythm, but the hosts should have taken the lead after 16 minutes when Gareth Barry smuggled the ball through for Lukaku, only for the Belgian to slide his finish just past the far post against his former club.
West Brom responded with their first opening moments later when Craig Dawson's cross picked out Darren Fletcher at the back post, but the Baggies skipper could only loop his header into the arms of Joel Robles.
Much of the pre-match talk had surrounded Lukaku, who last week became Everton's all-time leading Premier League goalscorer, but it was a difficult first half for the Belgian against an obdurate West Brom defence and he put another effort wide shortly before the half-hour mark.
Space was at a premium in the middle of the pitch as Everton probed for a way through, eventually forcing Ross Barkley into a couple of wayward long-range efforts.
The Baggies drew a first meaningful stop from Robles with just seven minutes remaining of the half when Nacer Chadli's low strike was turned past the post, but Everton were soon back up the other end and finally found the breakthrough moments later.
Barkley's first-time effort from the edge of the area was spilled by Ben Foster, and Mirallas was quickest to react to sweep the rebound home.
The Toffees felt that they should have had a penalty shortly afterwards when Seamus Coleman went to ground inside the area, but their unsuccessful claims were quickly forgotten when they doubled their advantage right on the stroke of half time.
Lukaku cut inside from the right flank and picked out Schneiderlin with a pass into the area, with the Frenchman beating his marker before burying the ball into the corner for his first Everton goal.
West Brom showed very few signs of fighting back from the two-goal deficit when the second half got underway, with Chadli coming closest to a response when his fierce drive was kept out by Robles.
It was Everton who looked the most likely to get the game's third goal, though, and Barkley almost provided it when he twisted and turned inside the penalty area before slamming his finish into the side-netting.
That third goal did arrive with eight minutes remaining, and it was Barkley who was the provider as he stood a cross up into the box for Lukaku to nod home for his 19th league goal of the season - his most ever in a single campaign.
It also took the Belgian level with Harry Kane as the league's top scorer this term, putting the seal on a fifth consecutive home victory in which they have now scored 18 goals and conceded just one.
Everton will now move above Manchester United in sixth with a win against Hull City next weekend, while West Brom slip seven points behind the Toffees having lost back-to-back games for the first time since December. body check tags ::