The striker scored the only goal of the game on 14 minutes as the Baggies inflicted a surprise defeat on Roberto Martinez's men
Salomon Rondon's first half goal was the difference between the sides as West Brom beat Everton 1-0 at Goodison Park on Saturday.
The striker chested home Jonas Olsson's header in the 14th minute to inflict a sixth Premier League home defeat of the season on the Toffees.
Ross Barkley and Tom Cleverley both struck the woodwork before half-time as Everton piled on the pressure, and the introductions of Arouna Kone and Gerard Deulofeu after the break failed to have the desired effect for Martinez.
But Tony Pulis' team remained resolute to end a run of five Premier League games without a win and claim a first away victory since October, while Everton failed to close the gap on the European qualification places.
A fast start from the unchanged hosts produced an early chance for Seamus Coleman. The full-back pounced as Darren Fletcher panicked in his own penalty area, only for Olsson to produce an impressive block.
Everton were in complete control, but found themselves behind when Albion scored on their first attack.
Olsson's front-post flick from Stephane Sessegnon's corner looped over Joel Robles and Rondon - one of four changes from last weekend's 1-0 defeat to Newcastle United - bundled the ball home.
Despite that early setback, Everton continued to dictate possession and laid siege to the West Brom goal before the break.
Ramiro Funes Mori was denied an equaliser by the legs of Claudio Yacob, before Ben Foster's fingertips kept out Aaron Lennon's deflected strike.
Even when Everton were able to beat the West Brom goalkeeper the woodwork denied them, with Barkley hitting the post with a fine curling effort before Cleverley's cross found the same upright having caught Foster out.
The second half brought no let up for the Albion defence as Everton continued to probe, James McCarthy the first to test Foster with a low drive from Lennon's pull-back.
Gareth Barry then saw an audacious strike fizz over the crossbar before Everton had a slice of luck as West Brom substitute Chris Brunt went agonisingly close to a second, his low shot nearly capping a swift counter.
Barkley and Barry were then both wasteful in promising positions, the later denied by a Jonny Evans block.
Kone and Deulofeu brought fresh impetus late on as Martinez threw everything at Albion, but West Brom were not to be denied a hard-earned victory.
- Goal