Villa came into the second leg of their semi-final tie leading 2-1.
Villa actually started the second leg quite brightly, but found the Baggies a tough nut to crack as they sought about getting the goal which would probably have put the game beyond their hosts.
Centreback Craig Dawson scored for West Brom with a 29th minute header.
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.
Villa win on penalties!
After two saves from Steer, Villa won the shootout with forward Tammy Abraham firing in the winning kick to send the team through to the final at Wembley Stadium.
This was quite some turnaround for the Villans' stopper, who earlier in the campaign was sent out on loan to Charlton Athletic, before being recalled due to injury.
Derby County have clinched their place in the Sky Bet Championship Play-Off Final following a 4-3 aggregate victory over Leeds United in the Semi-Final.
"There's obviously a lot of luck involved but wow - we practise penalties, so I think I must've faced 100 a day the last few days", Steer said.
Villa missed out in the playoff final previous year, losing 1-0 to Fulham and Grealish, who has been linked with a summer move to Tottenham, is keen to make amends in what could be his final game for the club. "All of us are very hungry".