Leeds and Derby are in the other playoff semi-final.
Villa won the first leg 2-1 at home but Craig Dawson's first-half header levelled it up for West Brom.
The final is at Wembley Stadium on May 27.
Despite the fact he'd only played limited minutes over the course of the season, the former Socceroos captain showed nerves of steel to smash his spot-kick into the bottom corner of the goal.
After the game, Aston Villa manager Dean Smith said of Steer: "It's awesome what can happen as Jed was at Charlton on loan earlier this year and now he's a hero for us".
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Tammy Abraham - Villa's striker on loan from English Premier League club Chelsea - netted the winning penalty to send the Birmingham club into the playoffs final for the second consecutive year. "We practice penalties, so I think I must've faced a 100 a day the last few days".
Leeds hold a 1-0 first-leg lead over Frank Lampard's outfit. "All of us are very hungry".
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.
Manchester City and Liverpool have proved themselves to be miles ahead of the rest of the Premier League over the course of the 2018/19 Premier League season, and Sky Sports pundit Keith Andrews has said they are the only two top tier sides that would not start Jack Grealish.