The Clarets' survival hopes suffered a major blow as rivals in distress Wolves left Turf Moor with the win that took them three points clear of Burnley and the last place in the relegation zone.
Wolves' third away victory of the season was a bitter pill for Burnley and a sell-out crowd to swallow as late fightback fell just short for Brian Laws and his men.
The Clarets had left themselves with a mountain to climb when they gifted Wolves an opening goal for Matt Jarvis and then fell further behind a minute into the second half through Adlene Guedioura's cruelly deflected shot.
But substitute Steven Thompson's first goal of the season with 17 minutes to go sparked a late onslaught as the Clarets threw everything at the visitors in a bid to hang onto their coat tails in the fight to beat the drop.
Fellow substitute Robbie Blake did his best to conjure up a point with a sparkling cameo which saw him hit the post and go close to an injury-time leveller.
But with Wolves hanging grimly on, the Clarets were left to rue another missed opportunity as the games begin to run out on their top-flight dream ahead of next Saturday's trip to Wigan and another potential escape route.
Steven Thompson heads in to spark a fightback
With injuries starting to bite, Laws was deprived of the services of Kevin McDonald and Jack Cork in midfield, as well as leading scorer Steven Fletcher.
That meant a re-call for Andre Bikey and Wade Elliott and the Clarets made an up-tempo start as they looked to build on their mid-week comeback against Stoke City.
Martin Paterson poked an effort wide and Chris Eagles drilled in a long-range effort which had Marcus Hahnemann scrambling to get the ball round the post.
Graham Alexander also tested the keeper from distance and Hahnemann was also forced to tip over a free-kick from Danny Fox as the Clarets strove for the opening goal.
With Wolves playing with just Kevin Doyle up front they were never over ambitious, although David Jones did get free to head weakly at Brian Jensen and when Doyle broke away Jensen went into the book for leaving his area to bring the striker down.
But a goal didn't look likely from the visitors until Burnley committed defensive suicide.
Danny Fox is stretched off with a rib injury
The Clarets have been their own worst enemies too often this season and so it proved again with 26 minutes gone.
Tyrone Mears tried to head the ball back to Jensen but was always struggling to get enough power on his mis-guided attempt and allowed Jarvis to by-pass the Clarets' keeper and walk the ball into the net for Wolves' first goal in four games.
Going behind again was the last thing Burnley needed and the goal unsurprisingly took its toll for a few minutes.
The Clarets also lost Fox to a rib injury but a minute before the break almost threw themselves a lifeline through David Nugent.
The in-form striker perfectly anticipated a knock-down from Clarke Carlisle from a Mears' free-kick and turned away from Christophe Berra but his bouncing shot agonisingly climbed to clip the top of the bar rather than hit the roof of the net to leave the Clarets with everything to do in the second half.
But if further proof was needed that Burnley's luck was out it came within a minute of the re-start when Wolves went 2-0 ahead.
David Nugent hits the bar on the stroke of half-time
The Clarets cleared a corner but when Wolves regain possession they worked the ball to Guedioura whose low shot was going well wide until it hit Carlisle and flew into the bottom corner.
Then at the other end when an instant reply was needed a cross from Paterson was blocked by the arm of Berra who got away without conceding a penalty.
Laws waited no time to make a double change with Thompson and Blake coming on for Bikey and Eagles.
Doyle could have wrapped it up with a chance on the break which he steered across the face of goal but at least the presence of Blake brought a bit of welcome guile to the Clarets' attempt to claw their way back into the game.
With 65 minutes gone Blake made the space to drive over a low cross which deceived Hahnemann and thudded against the foot of a post.
Chris Eagles tries to get Burnley moving forward
And then eight minutes later Thompson announced his arrival when he headed home to give Burnley a glimmer of hope.
Wolves cleared a cross from Mears but when Alexander put the ball back in, Thompson reacted well to glance in his first goal since last season's play-off semi-finals.
Suddenly the Clarets sensed some reward and piled forward and Alexander was close to an equaliser when Elliott laid the ball into his path for a shot which went just too high.
Wolves' substitute Michael Mancienne was close at the other end with a skidding shot which was well saved by Jensen.
But Burnley kept pushing and Leon Cort was just too high with a header from Blake's corner and the magical Blake stung the hands of Hahnemann before time ran painfully out.
All is not lost, though, and a win for the Clarets at Wigan next Saturday will keep the light at the end of the tunnel burning.
Burnley: Jensen, Mears, Fox (Jordan 40), Carlisle, Cort, Alexander, Bikey (Blake 55), Eagles (Thompson 55), Nugent, Elliott , Paterson. Subs: Duff, Edgar, Rodriguez, Weaver
Wolves: Hahnemann, Zuba, Craddock, Bera, Ward, Foley, Jones (Keogh 71), Henry, Jarvis (Ebanks-Blake 79), Guedioura (Mancienne 59), Doyle. Subs: Elokibi, Ebanks-Blake, Keogh, Vokes, Milijas, Hennessey.
Booked: Burnley: Jensen 13
Wolves: Guedioura 45, Mancienne 75, Berra, Keogh 83
Referee: Steve Bennett
Not our day