Ruben Neves' 67th-minute curling free kick looked to be enough for the visitors, who are now five points from sealing a place in the top flight.
However, Cardiff contrived to miss two penalties in stoppage time as Wolves held on for a famous win, in front of the biggest crowd for a Bluebirds game in over 40 years.
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Subs: Murphy, Manga, Pilkington, Mendez-Laing, Damour, Traore, Madine
WOLVES XI: Ruddy, Boly, Coady, Bennett, Doherty, Douglas, Saiss, Neves, Jota, Afobe, Bonatini
Subs: Norris, N'Diaye, Batth, Cavaleiro, Costa, Gibbs-White, Hause