The winger stepped up ahead of regular spot-kick taker Leighton Baines but blasted his effort against the foot of the post just before halftime after former Everton defender Joleon Lescott had been penalised for handball.
Mirallas did not emerge for the second half with Bryan Oviedo coming on.
Baines, who briefly consulted Mirallas before allowing the Belgian to take the penalty, has missed only one of the 16 spot-kicks he has taken in a Premier League game -- the first time coming in October against Manchester United.
Everton moved up one place to 12th but have now won one out of their last 13 matches in all competitions.
Not even a halftime video screen message from Hollywood great Sylvester Stallone, with the Goodison Park crowd filmed in a scene for the new Rocky film, could inspire Everton.
West Brom, who moved up to 14th and three points above the drop zone, are unbeaten in three league games since Tony Pulis took charge.
(Writing by Justin Palmer; editing by Alan Baldwin)
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