The Championship playoff final will take place on Sunday, May 26.
Jonathan Kodjia, meanwhile, will presumably be working on his dab in preparation for the final on May 27 at Wembley. Their second leg is on Wednesday, with Leeds protecting a 1-0 lead at their Elland Road home.
Villa will play Leeds or Derby for a chance to seal a spot in the Premier League.
West Brom was without suspended star striker Dwight Gayle but got a goal from Craig Dawson in the 29th minute to draw level.More news: Two coffees a day could help you live longer, research suggests
Brunt was dismissed in the 80th minute of Tuesday night's clash at the Hawthorns for a mistimed lunge on Villa midfielder John McGinn, earning him a second yellow card.
West Brom hung on throughout 30 minutes of extra time, but Steer's twin saves in the shoot-out meant Adomah's subsequent miss counted for little.
Villa goalkeeper Jed Steer made sure he was the hero on the evening by saving the first two West Brom penalties, and although the Birmingham based side had a wobble towards the end of the scheduled spot kicks, they eventually sealed their spot at Wembley. "We practice penalties, so I think I must've faced a 100 a day the last few days".
Villa win on penalties!More news: Black Mirror Season 5 Trailer Reveals Anthony Mackie And Andrew Scott Episodes
The Championship playoff final is regarded as the most lucrative match in world football with last year's clash between Fulham and Villa worth about £170 million (RM915.3 million) even if, as in Fulham's case, the victor is relegated after one season in the top flight.
"All of us are very hungry and have good legs in us".
Norwich and Sheffield United were promoted automatically after finishing as the top two in the regular season.More news: Brexit rebels tell Theresa May - Your EU divorce deal is dead