ALBION recorded their first clean sheet at Goodison Park for almost 30 years to bag their opening point of the season.
Ben Foster laid the foundations for the shut-out with a superb performance before debutant Luke Daniels picked up the baton for the final 13 minutes after the England keeper was forced off through injury.
Everton were on top in the first half but Albion had their chances to win it after the break, with Tim Howard denying James Morrison and Shane Long with impressive saves.
However, it was the Merseysiders who almost nicked the win late on, with Marouane Fellaini and Seamus Coleman both striking the wordwork.
New loan signing Scott Sinclair, who sealed his move from Manchester City less than 48 hours earlier, was immediately drafted into the squad, starting on the bench.
Steve Clarke rang one change to his XI, with Markus Rosenberg replacing Nicolas Anelka. Summer signing Diego Lugano was also selected among the subs for the first time.
Roberto Martinez named an unchanged team for his first home game in charge of Everton.
Shortly before kick-off, a minute’s applause was held in memory of legendary Everton striker Dave Hickson, who passed away in July.
Albion started confidently enough – but Foster was the first keeper called into action.
In the seventh minute, Jonas Olsson conceded possession just inside the Albion half and Everton fed the ball wide to Kevin Mirallas. The Belgian’s first-time centre was headed powerfully goalwards by Steven Pienaar, but the Baggies No.1 was equal to it.
Foster showed a safe pair of hands to deny the same player again a minute later, with the keeper diving low to his right to keep out the South African star’s 25-yard grass-cutter.
Albion showed plenty of endeavour during the opening stages but lacked cohesion in the forward areas.
Ross Barklay was seeing plenty of the ball and tried his luck from the edge of the box on 20, only for his right-footed drive to dribble wide of the far post.
The Baggies produced their first moment of note on 23 when a flowing move from the back, spearheaded by Youssouf Mulumbu, resulted in the DR Congo international curling the ball a couple of yards wide from 20 yards.
Two minutes later, the visitors threatened again when Morrison saw a 25-yard volley loop over after Long had flicked on Foster’s upfield punt.
Everton were back on the attack on 28 and after Barklay had drilled an inviting free-kick into the Baggies wall, Leighton Baines fired the rebound wide from 20 yards.
Foster had comfortably dealt with what Everton had thrown at him as the game passed the half-hour mark – but his team-mates owed him a debt of gratitude on 32. The England keeper produced a wonderful one-handed save to tip over Mirallas’ rising 18-yard drive from Coleman’s pull-back.
The former Blues keeper pulled off an equally smart save on 39 when he dived low to his left to clutch Coleman’s 15-yard drive just in front of his goalline after the Toffees right-back had been teed up by Pienaar.
At the other end, Morrison got away from Leon Osman on 44 but screwed a right-footed shot well wide from 25 yards.
Albion had to face a barrage of late Everton corners but held on to go into the break all square.
The visitors began the second half firmly on the front foot and a Graham Dorrans free-kick ricocheted goalwards off Fellaini before Coleman hacked clear.
However, Foster was soon called into action again, parrying Barklay’s awkward 20-yard drive before denying Fellaini from the rebound.
Mulumbu broke with purpose on 61 and fed Long in the box, but a wonderfully-timed Sylvain Distin challenge prevented the former Reading ace from firing goalwards.
Back came Everton and Foster was well positioned to clutch a fierce 15-yard Mirallas drive in front of his near post.
On 64, it was opposite number Tim Howard’s turn to impress. The American international superbly pushed away Morrison’s rising 20-yard drive after the Scotland international had exchanged a neat one-two with Rosenberg.
That proved the Swede’s final contribution, as he was replaced by summer signing Matej Vydra on 66.
Howard had to produce an even better save on 74. Morrison’s prod into the penalty area fell invitingly for Long whose 15-yard snapshot was brilliantly pushed away by the Everton No.24.
Albion suffered an injury blow on 77 when Foster limped off. He was replaced by Academy product Luke Daniels – who was granted his competitive first-team debut after more than nine years at the club.
The Baggies had an incredible escape on 82. Fellaini controlled Phil Jagielka’s diagonal ball into the box before poking it past Daniels, only for his effort to rebound back off the far post before Olsson hacked clear.
Daniels then came to Albion’s rescue, pushing Coleman’s low drive around his near post.
Everton hit the woodwork again in the first minute of stoppage time when Coleman’s mis-hit cross looped over Daniels and bounced down off the crossbar.
But the Baggies held on for a hard-earned point.
EVERTON (4-4-2): Howard; Coleman, Jagielka, Distin, Baines; Mirallas (Naismith 72), Osman, Fellaini, Pienaar; Barkley, Jelavic (Kone 72). Subs not used: Robles (gk), Heitinga, Deulofeu, Stones, Anichebe.
ALBION (4-4-1-1): Foster (L Daniels 77); Jones, McAuley, Olsson, Ridgewell; Rosenberg (Vydra 66), Mulumbu, Yacob, Dorrans; Morrison; Long (Brunt 81). Subs not used: Lugano, Berahino, Sinclair, Popov.
BOOKINGS: EVERTON – Barklay (foul 85). ALBION – Mulumbu (deliberate handball 28).
REFEREE: R East (Wiltshire).
ALBION STARMAN: Ben Foster.