Everton's home-grown youngster Leon Osman made Goodison Park forget about Wayne Rooney's possible departure with two crucial headed goals.
The 23-year-old midfield man lifted the gloom as Newcastle and Manchester United bid for England striker Rooney.
He was on target after two minutes from close range, only for Scott Dobie to quickly head Albion level.
But Osman was on the mark again after 69 minutes, deflecting home Lee Carsley's free-kick past Russell Hoult.
Everton fans, disappointed at Rooney's transfer request, received some early consolation as Osman put the Merseysiders in front.
Thomas Gravesen's long throw was headed on by Kevin Kilbane and the tiny figure of Osman arrived at the far post to head home.
Albion responded within four minutes as Jonathan Greening's corner flew past Nigel Martyn.
Dobie claimed the credit, but the last touch may have been applied by Carsley.
And, in an eventful opening, it took a point-blank save from Russell Hoult to block Joseph Yobo's header from eight yards.
Albion suffered a blow after 21 minutes when Thomas Gaardsoe was stretchered off after falling awkwardly under a challenge from Kevin Campbell and was replaced by Martin Albrechtsen.
Everton stepped up the pace after the break and Hoult needed to be alert to save Gravesen's shot.
Toffees manager David Moyes made a change after 61 minutes, taking off the tiring Campbell and sending on Duncan Ferguson.
And the home side then regained their lead after 69 minutes when Albrechtsen was punished for a foul on Ferguson.
Carsley's free-kick was fired into the centre of the penalty area and Osman was left alone to head past Hoult.
Everton: Martyn, Hibbert, Yobo, Stubbs, Pistone, Osman,
Gravesen, Carsley, Kilbane, Bent, Campbell (Ferguson 62).
Subs Not Used: Wright, Watson, Weir, McFadden.
Goals: Osman 2, 70.
West Brom: Hoult, Scimeca, Gaardsoe (Albrechtsen 23), Purse,
Robinson (Moore 64), Gera (Haas 54), Greening, Johnson,
Clement, Kanu, Dobie.
Subs Not Used: O'Connor, Kuszczak.
Goals: Dobie 7.
Ref: P Walton (Northamptonshire).