Chris Wood’s injury-time penalty kept the Clarets’ unbeaten home run going as Sean Dyche’s men refused to lie down.
A first Turf Moor defeat since New Year’s Day looked likely when Raul Jimenez scored with a superb 79th-minute volley to take Wolves closer to a European return.
But Burnley dug deep to keep alive their slim hopes of making it to Europe themselves with Wood keeping his cool to level from the spot following a handball from Matt Doherty as Sean Dyche’s battlers added another point to their collection and made it just one loss from 14 league games.