© PA Photos
Marouane Fellaini came closest to breaking the deadlock, but the Belgian saw his shot come crashing off the crossbar.
The breakthrough finally came in the 30th minute courtesy of another Leighton Baines special.
The England full-back linked up well with Steven Pienaar before belting a 20-yard shot past a helpless Ben Foster.
He was then given the chance to double Everton's advantage from the penalty spot after Claudio Yacob tripped up Victor Anichebe in the penalty box.
The Argentine had only been on the pitch a matter of minutes, as he had replaced young midfielder George Thorne, who was stretchered off.
Baines sent Foster the wrong way to put his team firmly in control at half time.
The Baggies came out a different side after the break but still found themselves second best. However, hope was restored by Shane Long with just under half an hour left to play.
Leon Osman missed a glorious opportunity to put the game to bed, but David Moyes's men were able to hang on with just the one-goal advantage.