Diogo Jota's first half goal and substitute Benik Afobe's chip after the interval secured the points for Wolves while Birmingham had captain Harlee Dean dismissed seven minutes after halftime for a foul on Helder Costa.
Wolves ended their six-year exile from the Premier League on Saturday when Fulham could only draw with Brentford.
They will be assured of the title if they avoid defeat against lowly Bolton Wanderers next Saturday.
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"It's a big moment for us, it's very important," Wolves manager Nuno Espirito Santo told Sky Sports.
"The players will celebrate like normal, but at the end of the season we'll have our deserved celebration."
While Wolves can start planning for life back in the top flight, Birmingham are in grave danger of slipping into the third tier of English football.
They are in 21st position, two points above the relegation zone but Barnsley, the team occupying the last relegation place, have a game in hand of Garry Monk's side.
(Reporting by Martyn Herman; Editing by Toby Davis)
