The Toffees sent out an early warning to the Reds with the win ahead of next month's FA Cup semi-final.
For most of the season the Toffees have toiled to recover from another characteristically slow start, but since the turn of the year they have generated significant momentum.
Just two defeats in 11 league matches has seen them rise to seventh and, although Liverpool can reclaim the advantage at Newcastle tomorrow, David Moyes' team have found form and confidence at exactly the right time.
The Everton manager insists the focus remains on improving their league position and not the all-Merseyside encounter at Wembley in a fortnight's time, and on current evidence he is right to do so.
It may not have been the most fluent of performances but importantly they got the job done with goals in either half.
Leon Osman may have his work cut out persuading the Premier League he should be credited with the first after a huge deflection off Gareth McAuley provided the decisive touch, but there was no doubt about substitute Victor Anichebe's second.
Aside from the hosts' 18th-minute opener, there were few incidents of note in the first half.
Osman, heading wide Leighton Baines' cross, and Darron Gibson, firing just over, both served early warnings to West Brom.
However, with Everton having exerted plenty of energy in booking an FA Cup semi-final place at Sunderland in midweek, it took the home side a while to find their fluency.
It came in ideal fashion as a good passage of possession play brought the goal and was probably the only period of the first half when they looked as though they were in real control.
When the ball was eventually worked to Osman in the inside right channel, he turned experienced defender Liam Ridgewell far too easily and offloaded to Nikica Jelavic on the edge of the penalty area.
The Croatia striker returned the pass and Osman fired goalwards only for the ball to take a huge deflection off McAuley and leave goalkeeper Ben Foster stranded.
West Brom's only chance of the half almost brought the equaliser when Tim Howard pushed Paul Scharner's shot into the path of Chris Brunt at the far post but the winger's attempt to smash home the rebound hit Shane Long and went behind.
Marouane Fellaini's low, long-range effort was tipped around the post by Foster before the Belgium midfielder reacted angrily to Keith Andrews raking his studs down his Achilles tendon but referee Peter Walton - in his final Premier League match before becoming general manager of the Professional Referee Organisation for the United States and Canada - awarded only a free-kick.
Magaye Gueye replaced Osman for the start of the second half but the early incidents all involved Jelavic.
He had a half-chance from a near-post header which Foster caught easily before he was booked for catching Ridgewell on the back of the head with his arm.
West Brom's left-back was also on the receiving end of a late tackle from Tim Cahill, who was yellow-carded.
The Australia international was then replaced by Anichebe with just over an hour gone.
Everton appeared to have lost their way with West Brom showing signs of improvement but Jonas Olsson's foul on Steven Pienaar, which also warranted a caution, presented a good opportunity to establish a cushion only for Jelavic to curl his shot over.
Anichebe showed his fellow striker how it should be done in the 68th minute when he fired in off the far post after Pienaar's diagonal run.
Pienaar should have put the result beyond doubt in the 74th minute having been played in by Jelavic but he shot straight at Foster.
Jelavic then headed wide Baines' shot and Gueye shot at Foster as, with the confidence of a two-goal lead, Everton attacked more fluidly.
Things were not so happy in the West Brom camp with Foster and Peter Odemwingie exchanging heated words as frustrations bubbled over late on.