Burnley put an end to any lingering fears of relegation with a win at Molineux that leaves Wolves on the brink of the drop to League One.
Danny Ings's left-footed strike gave Burnley an early lead which was doubled by Martin Paterson's close-range effort eight minutes after the break.
After Michael Duff's red card, Wolves substitute Nouha Dicko pulled one back.
But defeat leaves Wolves needing to beat Brighton, while hoping Barnsley and Peterborough both lose.
There was a mood of resignation at Molineux long before the final whistle precipitated a pitch invasion from around 500 fans. They protested against owner Steve Morgan before being quickly dispersed by police.
Happier hunting ground
Wolves had won 20 of the previous 27 meetings between the two sides. But the Clarets have improved that record recently - this was their third win at Molineux in six visits.
The home side had earlier made a bright start but were stunned on eight minutes when Burnley scored with their first real attack, Ings curling home a low left-foot shot from the corner of the box.
Wolves did not fold, however, and caused several moments of panic in the Burnley box.
But it was the visitors who came closest to scoring again when Ings's low cross was allowed to travel across the goal-line without anyone able to apply the finishing touch.
And, eight minutes into the second half, the worried Wolves fans' worst fears were realised when, after Ings's cross caused havoc in the six-yard box, Paterson swivelled to net Burnley's second.
Wolves boss Dean Saunders responded by making a double substitution on the hour, gambling on Bakary Sako, supposedly fit again after a hamstring injury that had looked to have ruled him out for the season, and Dicko.
Wolves' plunge to within a point of relegation came as Doncaster Rovers, the club Dean Saunders left in January to take over at Molineux, clinched promotion from League One.
"I am pleased for them that they have won the league," said Saunders.
"I walked into a mess there and had to sort that out. They cleared the decks and have come back up to the Championship and it's onwards and upwards for them."
And 10 minutes later he went for one last throw of the dice by bringing on Northern Irish teenager Liam McAlinden for his professional debut in place of Stephen Hunt.
McAlinden almost produced instantly when he curled a left-foot shot just wide with his first touch, then Karl Henry and Tongo Doumbia both fired just wide before young Burnley midfielder David Edgar made a superb block tackle to clear a six-yard box scramble.
Dicko briefly offered hope when he volleyed in from four yards with two minutes of normal time left but it turned out to be too little, too late as Wolves suffered their ninth defeat in 19 matches under Saunders.
Wolves manager Dean Saunders:
"I'm devastated we haven't got the right result. We've let two terrible goals in. And it's stacked up against us, but we're not dead yet.
"It's out of our hands now, which it wasn't before today, but stranger things have happened. Something happens every year. We've just got to try and make sure it happens to us.
"But we should never be in the position that we are in. Forget this game, we have got ourselves in a terrible position."
Burnley boss Sean Dyche:
"There is a big expectation here at Wolves. The demand from the fans about what the club should be can affect players and performances and make it awkward for the home team. Our game plan was to try and make the crowd nervous and hopefully make the opposition nervous.
"But we have our own expectations and I'm pleased with the way that the side found the clarity of thought to play rather than get involved in a scrap. There were some very good individual performances and obviously I was very pleased tactically at how we managed with 10 men.
"People who have seen us a lot will know that we have had some unbelievable bad luck. I've never seen as many big decisions go against us, we've had injuries and we have six contracts up. But we have managed to guide that group over the line."
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