West Brom enhanced their chances of avoiding relegation with a win which seriously dents Everton's prospects of Champions League qualification.
Thomas Gaardsoe headed against the bar for the home side in a disappointing game which only livened up when Zoltan Gera nodded in at the far post.
Gera might have conceded a penalty for a tug on Tim Cahill while Albion hit the post through Martin Albrechtsen.
Everton piled on some late pressure but the Baggies held on.
There was a frantic start to the match as West Brom chased Premiership survival and Everton looked to go four points clear of rivals Liverpool in the race for a place in Europe's premier competition.
Alessandro Pistone's rash early challenge on Geoff Horsfield almost cost Everton dear as Gaardsoe cushioned a header against the woodwork from Jonathan Greening's whipped in free-kick.
Gera nodded wide with the follow-up while Everton saw Marcus Bent's angled drive comfortably saved by Russell Hoult.
There was little to inspire the football purists at The Hawthorns and Everton were almost caught out by a long Baggies free-kick only for ex-Toffee Kevin Campbell's control to let him down and take him away from goal.
Both sides lacked the quality and invention to manufacture a breakthrough during a scrappy first half with West Brom's best chances coming from corner kicks.
The Baggies struggled to produce the recent good run which has given them a chance of avoiding relegation while Everton showed little sign of the form that has taken them to fourth place.
The Merseysiders were not helped by James Beattie's absence because of a medial knee injury picked up in training.
The man he may well have replaced Marcus Bent skied an effort disappointingly wide for Everton as they managed to string together a rare slick passing move and the miss proved costly.
Gera attacked a Greening cross at the far post and headed in to give Bryan Robson's side the lead.
West Brom's goalscorer was then fortunate not to concede a penalty as he looked to have tugged Cahill as the Everton midfielder threatened to go one-on-one with Baggies keeper Hoult.
The game finally began to open up and, at the other end, some neat skill by Kieran Richardson put Albrechtsen in on goal but his angled shot hit the foot of the post.
Bent had a powerful drive saved and shot just wide as Everton lay siege to the Baggies goal but to no avail.
West Brom: Hoult, Albrechtsen (Scimeca 89), Gaardsoe, Clement, Robinson, Gera, Wallwork, Richardson (Moore 86), Greening, Campbell, Horsfield.
Subs Not Used: Chaplow, Kanu, Earnshaw.
Goals: Gera 63.
Everton: Martyn, Hibbert, Stubbs (Watson 85), Weir, Pistone (Yobo 45), Osman, Carsley (Ferguson 75), Arteta, Cahill, Kilbane, Bent.
Subs Not Used: Wright, Plessis.
Booked: Cahill, Arteta.
Ref: G Poll (Hertfordshire).