It also earned Burnley their first away win of the season, having taken just one point from their previous five games on the road, as promotion-chasing Wolves suffered more problems in front of their own fans.
Wolves had shot up the table on the back of scoring seven goals in successive away wins at Stoke City and Crewe.
But they cannot rediscover that kind of form at Molineux where they have now collected just one point from their last three games.
They had plenty of chances to win the game but nine-goal leading scorer Carl Cort, who had been on target three times in the last two games, had a costly off night as Wolves missed out on a chance to move third in the table.
Their frustrations were perfectly summed up 11 minutes from time when Cort's knockdown was headed against the bar by Kenny Miller with Lee Naylor then also heading the rebound against the woodwork.
Irish midfielder Garreth O'Connor had given a sign of what was to come after just 15 minutes when his drive was well saved by Michael Oakes who seconds earlier had beaten away a volley by his namesake James O'Connor.
It was a warning Wolves failed to heed and, after Miller and Cort had both squandered clear chances, Burnley stunned Molineux with their historic strike.
Referee Steve Tanner awarded a free-kick just outside the area after Rohan Ricketts brought down James O'Connor.
Garreth O'Connor did not need a second invitation and he curled his shot around the wall and, this time, past Oakes.
Wolves took time to get to grips with the shock of falling behind but then proceeded to lay siege to the Burnley goal for the rest of the game for no reward.
Cort was particularly frustrated when he headed over the bar, saw a close-range shot beaten out by Brian Jensen and then was inches away from converting a Miller cross.
His agony in front of goal continued into the second half when he fired straight at Jensen from four yards only moments after unmarked central defender Joleon Lescott had sliced wide.