A goal of the season contender from Ashley Barnes was cancelled out by a late Raul Jimenez penalty at Molineux, as a dogged Clarets side were dramatically pegged back to a draw in the sweltering Wolverhampton heat.
After a tentative start to the game, it was the on-fire Barnes got the party started for the visitors, as the 29-year-old took charge of a loose ball on the edge of the Wolves area before hammering a spectacular right-footed effort on the half-volley into the bottom corner.
It was very nearly two moments later, when a Dwight McNeil cross from the left caused havoc inside a packed Wolves penalty area. Ben Mee's header across goal forced a back-peddling save on the line from Rui Patricio, but after his parry hit Ryan Bennett in the midriff, goal-line technology was required before the referee definitively ruled no-goal.
The story of the second half was a similar one, although Burnley created less as they were penned deeper and deeper into their own half with Wolves chasing an equaliser. For all their possession, however, the home side struggled to create anything of their own, with a speculative 20-yard effort from Morgan Gibbs-White the best they could muster in the first half hour of the second period.
As the home side stepped up their efforts to take something from the game, with Pedro Neto and Adama Traore thrown on along with the kitchen sink, they began to look somewhat more dangerous, and Diogo Jota found himself through on goal before some excellent recovery play from James Tarkowski prevented his effort even reaching Patricio.
In dramatic fashion, however, the home side did manage to steal away with a point, as Raul Jimenez - quiet for much of the evening - converted a penalty after a clumsy foul from James Tarkowski in the fifth minute of stoppage time.
Key Talking Point
Having conquered Torino in Italy during the week, it's looking as if Wolves will have to get used to the rigours of the Thursday-Sunday schedule that accompanies a Europa League campaign, and although many would suggest that their squad depth could be their downfall, they were able to make five changes to the side who started in Italy - while maintaining a strong-looking team.
Most notable among the changes was the re-introduction of midfield starlet Morgan Gibbs-White at the expense of Leander Dendoncker, while Matt Doherty returned at right wing-back. The usual front two kept their spots with Patrick Cutrone having to content himself with a place on the bench for the time being.
Whether it was fatigue or yet another tactical failure to break down a defensive set-up, however, they looked bereft of ideas throughout, failing to create much of note against a side who made them force the issue.
It's still very early in the season, and while Europe may understandably be the priority for now, the fact they remain winless domestically will come as a concern for Nuno Santo, who will know he soon needs to find a tactical solution to breaking down teams whose game-plan is to sit deep and frustrate.
They did find a way to take something from the match, however, which will come as a relief - and a let-off - after an uninspiring display at home.
Starting XI: Patricio (6); Bennett (5), Coady (6), Boly (5); Doherty (6), Gibbs-White (7), Neves (6), Moutinho (5), Jonny (5); Jimenez (6), Jota (6)
Subs: Dendoncker (5), Neto (5), Traore (5)
Star Man - Morgan Gibbs-White
It's hard to pick out a standout performer in what was a difficult afternoon to be a Wolves player, but in sweltering conditions, the 19-year-old's energy was tireless.
He kept things neat and tidy on the ball and showed some impressive industry off it, and although he'll have more creatively fruitful afternoons in his burgeoning career, he was the bright spark in a dull Wolves performance.
Key Talking Point
Sean Dyche started with the same XI who took Arsenal all the way last weekend, with the scintillating Barnes leading the line alongside Chris Wood, and with three goals to his name already this season, it didn't take the former long to find number four and get the Clarets off to a flying start.
13' GOAL!!! WHAT A STRIKE! McNeil cushions a lovely header into the feet of Barnes, who rifles the ball into the bottom corner past a stranded Patricio. 0-1— Burnley FC (@BurnleyOfficial) August 25, 2019
They certainly know how to play Wolves, having won their previous Premier League meeting back in March, and their dogged, organised approach made for a largely comfortable afternoon against a Wolves side who were given no space to play on the break. They could have been 3-0 up by half-time, with centimetres denying Mee's header and a great stop from Patricio denying Wood.
Their directness and physicality - a trademark of Dyche's Burnley - looked too much to handle for the home side, and even after their attacking threat waned deep into the second half, they looked untroubled at the back - their organised set-up an immovable object for a toiling Wolves side.
It was ultimately heartbreaking for Burnley who had held on so valiantly, but four points from an exceptionally tough opening three matches suggests they will have very little to worry about for the season ahead.
Starting XI: Pope (6); Lowton (6), Tarkowski (7); Mee (6), Pieters (6); Gudmundsson (6), Cork (6), Westwood (6), McNeil (6); Barnes (6), Wood (7)
Subs: Lennon (6), Rodriguez (6)
Star Man - Ashley Barnes
Having started the season in the form of his life, it's now 12 goals in Ashley Barnes' last 18 appearances for Burnley, and he was a constant menace to the Wolves' back three who categorically failed to deal with the threat posed by him and Wood.
Ashley Barnes does not get enough credit that he deserves 13 goals in 2019 alone thats progression right there he's 29 not bad.— Ődoistá (@Odoista) August 25, 2019
His early strike was utterly sublime, and characteristic of the sort of form he's shown so far this season, and even though he faded out of the game as his side were forced ever-deeper into their own half, he's been nothing short of a revelation.
If Burnley are to live up to their early promise, then his goals will be a key piece of the puzzle.
Europa League duty beckons for Wolves, as they welcome Torino to Molineux looking to finish the job and qualify for the Europa League proper. They then have another Super Sunday on their hands, as they travel to Merseyside to take on Everton.
Burnley, meanwhile, take on Sunderland in the Carabao Cup on Wednesday, before league leaders Liverpool visit Turf Moor for the evening kick-off on Saturday.