Lyle Foster's 95th-minute heroics for Burnley broke the hearts of a spirited Wolves side that came back from two goals down in the first half, as the 3-2 defeat condemned Vitor Pereira's side to remain the only winless side in England's top four divisions.
Burnley looked to be cruising to victory after two Zian Flemming goals until Jorgen Strand Larsen's penalty and Marshall Munetsi's header levelled terms just before half-time.
But Foster's last-gasp winner secured three vital points for the Clarets as boos rung out around Molineux.
Burnley started the first half in fine fashion as Flemming's early double came thanks to two gorgeous Quilindschy Hartman assists. The opener, a beautifully cushioned volley from the Dutchman's long searching ball, was the goal of the day, and confidence was high for Burnley after Flemming tapped his second home easily after half an hour.
The Clarets' resolute defence eventually gave way when Josh Cullen caught the back of Santiago Bueno's heel, allowing Strand Larsen to convert his first Premier League goal of the season with aplomb.
Jean-Ricner Bellegarde, returning to the side after an injury, was at the centre of much of the home side's attacking play, and it was his neat footwork and cross that created the second as Ladislav Krejci's volley across the box was bundled home by a determined Munetsi to end a frantic first half.
Chances were few and far between for both sides in the second period, bar a Jon Arias free-kick that rattled the bar, and the point looked wrapped up for both sides until a sensational Hannibal through ball unlocked the Wolves defence and allowed Foster to slot under Sam Johnstone and send the travelling fans into a frenzy in the 95th minute.
The action wasn't over yet, though, as Martin Dubravka had to make a diving save from Bueno with the last kick of the game to wrap up the points for Scott Parker's side.
The result was greeted by boos all around Molineux, as Wolves stay rock-bottom of the Premier League, while Burnley pick up an invaluable three points that takes them five points clear of the drop zone after Nottingham Forest's loss to Bournemouth.
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