Midfielder Youssouf Mulumbu scored his seventh goal of the campaign after just 10 minutes as the Baggies finished their Hawthorns programme on a successful note.
Everton had substitute Diniyar Bilyaletdinov sent off late on after just five minutes on the pitch for a challenge on James Morrison.
Roy Hodgson's side are now four points clear of local rivals Aston Villa, who visit Arsenal on Sunday, thanks to a dramatic turnaround in fortunes under the former Liverpool manager.
They have collected 19 points from 11 games since he replaced Roberto Di Matteo in early February and been beaten only twice.
The game was an open affair with both sides free from the threat of relegation and opposing strikers Peter Odemwingie and Victor Anichebe were a constant threat.
It was surprising only one goal was scored given the chances created by both sides.
Albion midfielder Paul Scharner was a distinctive figure with his new dyed blue and white haircut in Albion colours, while Baggies leading scorer Odemwingie received his Barclays player of the month award before kick-off.
The first threat came from Odemwingie after he raced onto a long pass from Mulumbu but he drilled his shot into the side netting.
But after 10 minutes Mulumbu broke the deadlock.
Chris Brunt chipped the ball forward and Odemwingie held off the challenge of Sylvain Distin before squaring the ball across the area to Mulumbu who had a simple tap-in.
Everton had the chance to equalise four minutes later when Anichebe spun past Jonas Olsson inside the box but Scott Carson made a fine save to deflect his shot past the post.
Everton keeper Tim Howard then tipped a Brunt free-kick over the bar after Leighton Baines had brought down Odemwingie.
There were plenty of chances at both ends and John Heitinga headed wide from close range when unmarked from a Seamus Coleman cross.
Jerome Thomas then skipped past Tim Howard inside the Everton box but saw his shot cleared off the line by Tony Hibbert.
Howard made a fine save to keep out Odemwingie's header at point blank range after Olsson had flicked on a long throw from Mulumbu.
Carson made another fine save to turn aside Anichebe's downward header low to his left from a Hibbert cross
Everton skipper Phil Neville became the first player to be yellow carded in the 49th minute for a challenge on Mulumbu.
Everton were on top early in the second period and a deep corner from Arteta found Leon Osman completely unmarked but he sliced his shot wide.
In an Albion counter-attack Cox just failed to connect at full stretch with a low centre from Odemwingie.
Neville appealed in vain for a penalty for handball after his volley struck Scharner. Then Tamas made a great block to keep out a fierce drive from Arteta.
Thomas was booked for bringing down Hibbert before Jermaine Beckford replaced Coleman after 62 minutes.
Scharner could have doubled Albion's lead but headed wide from Odemwingie's ball into the danger area.
Phil Jagielka climbed above the Baggies defence to head an Arteta corner over the bar.
Albion were sitting too deep and Bilyaletdinov shot over from 10 yards out after racing onto Hibbert's cross.
Bilyaletdinov was sent off after 77 minutes for a high challenge on Morrison.
Howard denied Odemwingie who went for goal with Brunt unmarked in the centre before Tamas was booked in the final minute for time wasting.