The defeat means Wolves must beat Brighton on the final day of the season and hope results elsewhere go in their favour if they stand any chance of staying up.
However, Burnley have secured Championship status for another season as the win moves them on to 58 points with one game remaining.
Danny Ings gave Burnley the lead within eight minutes. This advantage was doubled by Martin Paterson?s second half strike.
After Burnley defender Michael Duff was sent off, Wolves found a consolation goal through substitute Nouha Dicko.
Though Wolves started brightly, they fell behind through Ings? goal. The striker curled an effort beyond the Wolves goalkeeper for the opener.
Wolves did not fold but, although they caused a few moments of panic in the Burnley penalty area, they were fortunate not to go further behind at the break. Ings? low cross travelled right across the face of goal and just needed a simple finish.
Burnley?s confidence grew and they were able to add to their lead minutes into the second period.
Former Stoke striker Martin Paterson swiveled to turn home another dangerous Ings cross. Wolves? supporters fears of the drop worsened. A dark, grey cloud loomed over Molineux.
In a desperate attempt to lift it, Wolves boss Dean Saunders brought on winger Bakary Sako, not fully fit after a recent hamstring injury, and striker Dicko.
Liam McAlinden, another home sub, came close for Wolves with a curling effort from range but saw it fizz wide.
Although Dicko netted when he fired home from four yards out, Wolves couldn?t avoid their ninth defeat in 19 matches under Saunders and it makes the final day of the season very desperate indeed for their fans.