In-form Everton saw off a frustrated West Brom with a goal in each half to climb above Mersey rivals Liverpool in the Premier League table.
Leon Osman's wayward 20-yard shot, after a slick one-two with Nikica Jelavic, deflected off Albion's Gareth McAuley past a stranded Ben Foster.
Everton's recent PL record
And Victor Anichebe's low strike capped a great week for FA Cup semi-finalists Everton, who move up to seventh.
Albion's best chance saw a fierce shot by Paul Scharner parried by Tim Howard.
Historically Everton have been slow out of the Premier League blocks before picking up the pace in the second half of the season.
And this term is no different, with Moyes' men losing just two of their last 15 matches to move above Liverpool,
who play Newcastle on Sunday,
and book a mouth-watering FA Cup last-four tie against their neighbours.
Moyes told his players not to become distracted by
the Wembley date,
a message supported by skipper Phil Neville, and a lively performance indicated the pair's pre-match warnings had been heeded.
A congested midfield area allowed Everton's full-backs to storm forward and provide the main attacking outlet for the home side in the opening stages.
Moyes pleased Everton avoided 'FA Cup hangover'
Inevitably, Osman's opener started down the flank as right-back Tony Hibbert slipped in a pass to the midfielder, who smartly turned away from his marker before speculatively shooting towards goal.
Despite their relative success in the Premier League and FA Cup so far this term, Everton remain troubled by a lack of attacking incisiveness.
Only Stoke and Wigan have been less prolific in front of goal and there was a sense in the opening hour that the Toffees may come unstuck despite another dominant performance.
However, these feelings proved unfounded as substitute Anichebe wrapped up the victory six minutes after his introduction.
Steven Pienaar, back in the side after being cup-tied for the midweek
FA Cup quarter-final win at Sunderland,
was the architect as he sliced through a static West Brom backline before feeding the Nigerian, who drilled a 20-yard shot off the post.
DID YOU KNOW?
Referee Peter Walton took charge of his final Premier League match before heading to the United States to become Major League Soccer's officials' chief. An emotional Walton, 52, was close to tears at the final whistle and was embraced by David Moyes and Roy Hodgson.
Away days have been profitable for 14th-placed West Brom this season, with only Manchester United, Manchester City, Arsenal and Tottenham boasting better records on the road.
But they struggled to hit Everton on the break and only Scharner saw a clear sight of the home goal.
The Austrian skipped unopposed into the Everton box before his fierce low drive was parried wide by Howard. Chris Brunt's rebound looked to be heading towards goal but it struck Baggies team-mate Shane Long who could not move his body out of the way.
Frustration got the better of West Brom late on when Peter Odemwingie clashed with his own keeper Foster after the Nigerian reacted angrily to criticism.
Odemwingie blasted into the side-netting from an acute angle in Albion's best second-half chance but, in truth, they never looked like clinching a win which would have moved them mathematically closer to Premier League safety.
Second goal killed off game - Hodgson
Everton manager David Moyes:
"It was a great result for us today.
"After the performance in midweek I was a little concerned, mentally more than physically, about how we would get on today.
"But the players did a brilliant job to go on and get an important three points.
"West Brom have a great away record and I was aware of that."
West Brom head coach Roy Hodgson:
"I think we played quite well in the first half and unlucky to go 1-0 down to the deflection.
"We were reasonably in control in the first half.
"But the second goal allowed Everton to play with more confidence. After that we found it difficult to get back into the game.
"Our work-rate was good, we worked very hard, but we were playing against a good team. This is a hard place to come."
- 24 Howard
- 02 Hibbert
- 03 Baines
- 05 Heitinga
- 06 Jagielka
- 04 Gibson
- 17 Cahill Booked (Anichebe - 62' )
- 21 Osman (Gueye - 46' )
- 22 Pienaar
- 25 Fellaini
- 07 Jelavic Booked (McFadden - 87' )
- 01 Mucha
- 15 Distin
- 18 Neville
- 11 Stracqualursi
- 14 McFadden
- 19 Gueye
- 28 Anichebe
West Bromwich Albion
- 01 Foster
- 03 Olsson Booked
- 06 Ridgewell
- 23 McAuley
- 28 Jones
- 05 Tchoyi (Fortune - 73' )
- 08 Andrews
- 11 Brunt (Cox - 77' )
- 33 Scharner (Dorrans - 67' )
- 09 Long
- 24 Odemwingie
- 19 Daniels
- 20 Shorey
- 25 Dawson
- 17 Dorrans
- 21 Mulumbu
- 31 Cox
- 32 Fortune