Romelu Lukaku’s stunning early strike against his former loan club and a hopeful drive from Kevin Mirallas wrapped up the points for Roberto Martinez’s side and forced ex-Goodison Park coach Alan Irvine back to the drawing board.
In just the second minute, Jonas Olsson scuffed a clearance to the edge of the box and Lukaku curled a sumptuous effort around Ben Foster and into the corner of the net.
Everton were rattled at times as they looked to secure a first clean sheet and three-point haul of the campaign, but they made the result safe on 66 minutes as Mirallas sent in an ambitious effort which somehow slipped under the body of a red-faced Foster.
Foster had shrugged off a thumb problem which forced him out of England duty to start, while James Morrison made his first league start of the season, replacing the injured Youssouf Mulumbu for West Brom.
Stephane Sessegnon was ruled out with blurred vision after taking a ball in the face during training on Friday.
Joleon Lescott failed to make the squad, despite returning to full training after a knee injury, while fellow summer recruits Georgios Samaras and Sebastian Blanco made the bench.
Everton made one change from their 6-3 defeat by Chelsea with John Stones replacing Sylvain Distin at the back.
And the visitors were ahead after just one minute and 40 seconds as Lukaku seized on a mistake from Olsson.
The defender’s awful clearance fell straight to the striker who beautifully curled past Foster from 18 yards.
It was Lukaku’s first Everton goal since making a permanent move from Chelsea but he was apologetic in his celebrations, having spent the 2012/13 season on loan at The Hawthorns.
Albion tried to respond and Saido Berahino’s effort was deflected over as, with the home fans restless, they began to dominate.
There were brief signs of a blossoming partnership between Brown Ideye and Berahino but, for all their bluster, the hosts lacked the quality to seriously threaten Everton.
Chris Brunt hit the side netting and Berahino’s shot deflected wide after 33 minutes but Tim Howard remained untroubled.
Everton’s threat was minimal but Mirallas warned of what was to come when he fired over from 25 yards eight minutes before the break.
Lukaku followed suit in first-half injury time and Naismith should have made it 2-0 five minutes after the break.
Foster’s fine low save from Lukaku presented the Scotland striker with a gaping goal six yards out, only for him to balloon over. It was a huge let-off for the Baggies but one they did not heed.
Everton grew increasingly comfortable with the hosts’ predictable attacks and doubled their lead following another howler from Albion after 66 minutes.
Mirallas’ tame effort from 25 yards out should have been easy for Foster but the England keeper allowed it to creep under his body.
From then it was easy for the visitors and Aiden McGeady shot wide on 73 minutes as the fight left the Baggies.
Samaras and Blanco made their debuts but could not make the difference and Foster saved well from Leon Osman to deny Everton a third.
The keeper thwarted the midfielder again on 88 minutes with a fine low stop after a sweeping Toffees move cut the hosts apart.
And the underemployed Howard had the final say when he denied Berahino and Samaras a consolation in injury time.