Chris Wood's 96th-minute penalty secured a 1-1 draw for Burnley to dent Wolves' Champions League hopes.
Adama Traore combined with Matt Doherty for the game's opening goal as the Republic of Ireland full-back's shot deflected off James Tarkowski and landed perfectly for Raul Jimenez to volley beyond Nick Pope in the 76th minute.
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But in a dramatic finish at Turf Moor, referee Mike Dean penalised Doherty for a handball as Wood stepped up to restore parity. It was Burnley's only shot on target in the game.
The result means Wolves remain in sixth place, three points off Manchester United in fifth and Leicester in the fourth and final Champions League place. It is now just one defeat in 14 league games for Burnley, who remain 10th after Arsenal's 2-1 win over Liverpool later on Wednesday.
Burnley: Pope (6), Taylor (6), Bardsley (6), Tarkowski (7), Long (7), Pieters (7), Westwood (6), Brownhill (6), McNeil (6), Rodriguez (6), Wood (7).
Subs: Gudmundsson (6), Brady (n/a), Vydra (6)
Wolves: Patricio (6), Saiss (6), Boly (6), Coady (6), Vinagre (7), Traore (7), Moutinho (7), Neves (7), Podence (7), Jota (6), Jimenez (8).
Subs: Doherty (7), Neto (n/a), Jonny (n/a), Dendoncker (n/a)
Man of the match: Raul Jimenez.
Late penalty dents Wolves' top-four hopes
These founder members first met in the third week of the first ever Football League season in September 1888, and both still harboured European ambitions as established top-flight sides heading into the encounter.
Burnley manager Sean Dyche spoke in the build-up of being focused on trying to extend his side's five-match unbeaten run but it was Wolves who shaded a first half low on goal-mouth action.
Burnley named an unchanged side as Chris Wood partnered Jay Rodriguez in attack, while Kevin Long continued to deputise for injured captain Ben Mee in defence.
Wolves brought Adama Traore back into the starting line-up as one of four changes from the 3-0 win over Everton. Ruben Vinagre, Joao Moutinho and Diogo Jota were also restored in place of Matt Doherty, Jonny Otto, Leander Dendoncker and Pedro Neto.
Traore, deployed as a right wing-back by Nuno Espirito Santo, produced the game's first chance after 10 minutes when his hanging cross was met at the far post by Jimenez but his header was comfortably held by Nick Pope.
Moments later, the visitors ought to have been in front when Romain Saiss headed over with his back to goal from two yards out from an inswinging Joao Moutinho corner.
Burnley were forced into a change after half an hour as the injured Charlie Taylor was replaced by Johann Berg Gudmundsson, but it was Wolves who continued to threaten the breakthrough as Diogo Jota collected Daniel Podence's lofted pass only to scuff his shot wide of the post.
The Clarets had offered very little as an attacking threat, aside from a rising shot from Jay Rodriguez, and the striker was also forced off shortly after the restart with a calf strain to add to Burnley's growing injury list.
The hosts won this fixture 2-0 at Turf Moor last season, but that remains their only top-flight home victory against Wolves since 1963 - and the visitors came close again when Traore blasted his shot wide from the angle two minutes into the restart.
Ruben Neves made a fine last-ditch block to deny Josh Brownhill shortly after Rodriguez's withdrawal, but Wolves regained the initiative shortly before the second drinks break as Jota set up Podence for a right-foot shot that flashed just wide.
With 14 minutes remaining came the game's one moment of class.
Jimenez broke the deadlock as the Mexican readjusted his body to meet the ball knee-high and fire past Pope to become the first Wolves player to score 17 top-flight goals in a season since John Richards in 1975/76.
Wolves had barely been troubled all evening, but in the third minute of stoppage time, Matej Vydra's knockdown was missed by Rui Patrico, only for Wood to somehow head wide with the goal at his mercy. The striker did not dwell on the glaring miss, however, as after referee Dean spotted Doherty's handball, he stepped up to confidently dispatch his spot-kick high into the net.
What the managers said
Burnley boss Sean Dyche: "Another interesting twist went our way and we produced another good finish to a game which had its problems with the injuries. To come out with a point against a really good side from the challenges we're having is really pleasing.
"Woody showed a great mentality and he grew into the game. When he missed the chance, it goes to show you what a strong character he's got to step up and score the penalty. I was a long way from the incident, but I've looked back at it and it does look a clear case of handball."
Wolves boss Nuno Espirito Santo: "We had plenty of the ball and created some great situations and it was a fantastic goal from Raul. It's always hard to take... every goal you concede is hard to take and a goal in the final moments is even harder.
"I always felt we were in control and the team played well. Sometimes, justice doesn't exist in the game, this is football. The players completed well but we have to now focus on the next game.
"I don't live based on ifs, I live based on reality and the reality is to prepare for the next game. I'll only be thinking about that."
Man of the match - Raul Jimenez
Pope had kept 14 clean sheets for Burnley this season - but there was nothing he could do about Jimenez's sumptuous strike that would have moved Wolves onto 58 points.
That would represent their highest total in a Premier League campaign, bettering last year's tally of 57 - but they will have to now try to achieve that in their final two games.
Jimenez had produced a fine overall display prior to the strike, producing three shots, but it was only after his late withdrawal that Burnley snatched a dramatic late point. Only Mohamed Salah has scored more Premier League goals in 2020 than Wolves' Jimenez (9).
- Burnley are unbeaten in their last seven Premier League games at Turf Moor (D3 L4); their longest run without a home defeat in the competition.
- Since beating Burnley in their first Premier League meeting under Nuno Espirito Santo (1-0 in September 2018), Wolves have gone winless in the three such meetings since (D2 L1).
- This was the 26th time this season that both Burnley and Wolves have failed to score in the first half of a Premier League game - no team have failed to do so on more occasions.
- 73 per cent of Wolves' goals in the Premier League this season have been scored in the second half (36/49); the highest percentage of any side.
Live Premier League
Norwich host Burnley on Saturday at Carrow Road, live on Sky Sports Premier League (kick-off 5.30pm). Wolves host Crystal Palace on Monday at Molineux (kick-off 8.15pm).