As both sides failed to pursue their European ambitions, Chris Wood scored a dramatic stop-time penalty to secure a draw with Wolves.
Into the top corner after a handball by Matt Doherty, Wood fired his spot-kick in the 96th minute.
Raul Jimenez had brought Wolves ahead with a superb volley from the edge of the box, after 76 minutes.
At one point on a place in the Champions League, Nuno Espirito Santo’s side had closed the gap, playing a game more than rivals Leicester City and Manchester United.
Burnley have their own Europe League hopes. The club almost leveled when Wood was stranded with keeper Rui Patricio nodding wide of an open target.
And moments later a hopeful cross hit Doherty on the arm and his penalty was not misunderstood by the New Zealand international.
While Wolves remain sixth and three points off the top four, Burnley is sitting ninth in the Premier League.
Burnley 1 – 1 Wolves
Goals: 0-1 Jimenez 76′, 1-1 Wood 90+6′
Yellow cards –
Burnley: Pope, Bardsley, Long, Tarkowski, Taylor, McNeil, Brownhill, Westwood, Pieters, Woord, Rodriguez
Wolves: Patricio, Coady, Boly, Saiss, Vinagre, Moutinho, Neves, Traore, Podence, Jimenez, Jota