Ireland international Shane Long put Albion in front after three minutes, controlling Chris Brunt's long ball superbly as it dropped over his shoulder before turning to fire past keeper Brad Guzan.
Eight minutes later Long seized on a misplaced midfield pass from Villa's Leandro Bacuna to charge through the defence and chip the ball home for his second goal.
Stephane Sessegnon then missed from four metres for West Brom before Villa turned round a different side after the break.
Karim El Ahmadi reduced the deficit from close range and Ashley Westwood produced a fierce long-range drive - his first goal for Villa - to level in the 76th minute.
Both teams have 15 points from 12 games, Albion in 11th place and Villa in 12th.
Leaders Arsenal are four points clear on 28.
(Reporting by Tony Goodson; editing by Tony Jimenez)
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