The Toffees, who climbed above neighbours Liverpool into seventh, took the lead when Leon Osman's shot took a huge deflection off Gareth McAuley. Osman's effort looked to be heading off target before McAuley's attempted intervention.
Victor Anichebe came off the bench to complete a deserved victory after 68 minutes and help secure Everton's third win in a row in all competitions.
Steven Pienaar returned to the Everton starting line-up, having been cup-tied for the 2-0 FA Cup win over Sunderland. Tony Hibbert and Phil Jagielka also returned to the side as David Moyes made three changes.
Somen Tchoyi was handed his first West Brom start in five months with Roy Hodgson making four changes to the side that lost 3-1 to Newcastle United last weekend. Paul Scharner, Chris Brunt and Shane Long were also restored to the starting line-up as Hodgson opted for an attacking 4-4-2 formation.
The home side dominated the first-half and showed early intent when Osman glanced a fine left-wing cross from Leighton Baines just wide.
Two minutes later some intricate build-up play saw the lively Pienaar combine with Baines before laying the ball off for Darron Gibson, who fired just over the bar from the edge of the area.
Everton took the lead after 18 minutes as Osman played a neat one-two with Nikica Jelavic before seeing his shot take a big deflection off McAuley. The build-up play was something to behold even if there was more than an element of fortune about the goal.
West Brom were struggling to make an impact at the other end although they almost scored with their first real attack after 27 minutes. Scharner broke into the area and forced a good low save from Tim Howard. The ball rebounded out to Brunt whose goal-bound shot hit team-mate Long and went out for a goal kick.
Everton immediately launched an attack of their own and Ben Foster had to be on his guard to push a well struck Marouane Fellaini shot out for a corner.
The second-half started in tepid fashion, with little action of note until some excellent play from Jelavic saw the Croatian backheel the ball to Pienaar, who was denied by Foster as he ran through one-on-one with the goalkeeper.
The Toffees made the game safe when man-of-the-match Pienaar dribbled the ball to the edge of the area and found Anichebe, who fired first time across goal and into the bottom left corner.
It was a cleanly struck shot from Anichebe, who came off the bench against West Brom in January to score the winner in the reverse fixture.
Foster was West Brom's best performer and he produced a fine save at his near post to keep out a powerful shot from Magaye Gueye.
The Baggies struggled to create chances and there was an inevitability about the result once Anichebe had doubled Everton's lead.
Frustrations boiled over late on as Foster and Odemwingie engaged in a heated argument, with the goalkeeper unhappy at the Nigerian's marking on a corner kick.