West Bromwich Albion goalkeeper Ben Foster produced an inspired performance to deny Roberto Martinez a first competitive victory as Everton manager.
Foster twice frustrated Steven Pienaar and Kevin Mirallas and also saved shots from Seamus Coleman, Ross Barkley and Marouane Fellaini at Goodison Park.
The Baggies' best chance fell to James Morrison, who was denied by Tim Howard.
Clarke satisfied with hard-fought point
Foster limped off with a foot injury late on, before Fellaini and Coleman struck the West Brom woodwork.
While Foster's afternoon ended in disappointment, his departure led to a Baggies debut for Luke Daniels, who has been at West Brom since 2004 but has had seven loan spells away from the club.
Albion manager Steve Clarke later said Foster
"felt something pop"
in his foot, and the Baggies boss faces a potential problem in goal and up front.
West Brom were hoping to build on their highest Premier League finish of eighth in 2012-13, but they have only collected one point from their opening two matches and failed to score a single goal.
Romelu Lukaku, who scored 17 Premier League goals during a season-long loan at The Hawthorns, has returned to Chelsea and his replacement, Nicolas Anelka, has hinted he
may retire after the death
of his agent Eric Manasse earlier in the week.
Another Everton draw
Everton drew 15 times in the Premier League in 2012-13, the same amount as Stoke and more than the other 18 sides in the division
The Toffees have started this campaign in the same vein, with two draws from their two matches this season
Anelka was given compassionate leave and replaced by Markus Rosenberg but the Swedish striker, who has now failed to score in 29 games for West Brom, was ineffective up front.
But the duo were unable to help their side to victory as Foster, with England manager Roy Hodgson watching, repeatedly frustrated the hosts.
He blocked Pienaar's diving header and then a low effort from the South African, before tipping a Mirallas shot over the crossbar.
Foster continued his excellent performance after the break as he produced a fine double save when he parried Barkley's low drive and then quickly recovered to deny Fellaini's follow-up.
Everton 0-0 West Brom: Roberto Martinez frustrated by stalemate
But the goalkeeper hobbled off 12 minutes from time to be replaced by Daniels.
And the debutant was lucky not to be picking the ball out of the net soon after coming on as Fellaini curled a close-range shot against the foot of the post, before Coleman's mis-hit cross hit the bar in injury time.
Everton manager Roberto Martinez:
"It's fair to say we were frustrated, if you look at the amount of possession we had and the opportunities we had.
"West Brom were really organised and stayed deep, trying to counter-attack, but we coped with their threat really well.
"We had the chances to win the game, we deserved a win and we deserved three points. We were magnificent off the ball."
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