But before they got off the mark, it was Albion who held the attacking reins and they guaranteed a nail-biting finish with a late penalty.
West Brom fired in a string of shots in the one-sided first half with keeper Tim Howard making two fine stops to deny striker Ishmael Miller.
But Everton were a different proposition after a half-time roasting from David Moyes and they finally began to probe the Albion defence for cracks.
They had a goal disallowed in the 64th minute when Jack Rodwell found the target with a powerful header only for referee Rob Styles to rule he was guilty of pushing.
But they kept their heads high and took the lead just 60 seconds later with a cracking drive from Leon Osman.
Mikel Arteta engineered the move as he beat his man to slide a perfect pass to Osman and he gave keeper Scott Carson no chance with his well placed angled shot.
Everton stretched their lead in the 76th minute when defender Joleon Lescott thumped a long ball through the middle to find striker Ayegbeni Yakubu.
He shrugged off a weak challenge from Abdoulaye Meite to head the ball over the advancing Carson and into the back of the empty net.
Tony Mowbray's men were down but they continued to battle and they should have reduced the arrears in the 86th minute when Roman Bednar gained possession just ten yards out.
Bednar twisted on the spot to fire in a shot but the ball flew wide of the far post when it looked easier to find the back of the net.
Bednar then got his name on the scoresheet in the 89th minute when Everton captain Phil Neville needlessly handled in the area.
Referee Styles immediately pointed to the spot and Bednar made no mistake with his penalty, but it was too late for Albion.
Moyes still has £20million in the pot to spend on new players before the transfer curtain comes down and he will need to make a plunge into the market after this smash-and-grab raid at The Hawthorns.