Former Real Betis manager Mel, who picked Nicolas Anelka despite a club row with sponsors Zoopla over the former France striker's alleged anti-Semitic gesture in a match last month, watched his side go behind in the 41st minute.
Romelu Lukaku headed the ball down just outside the penalty box for fellow Belgian Kevin Mirallas and the winger ran on to beat West Brom keeper Ben Foster.
Uruguayan Diego Lugano equalised for the hosts in the 75th minute with a near-post header following a right wing cross by James Morrison.
Everton thought they had grabbed the winner with the final kick of the game but defender Sylvain Distin was ruled offside after touching in Gareth Barry's shot from close range.
The draw lifted West Brom from 14th to 13th in the table while Everton stayed in sixth position, nine points adrift of leaders Arsenal with 16 games remaining.
(Writing by Tony Jimenez; editing by Pritha Sarkar)
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