Wolves continued their revival but left the Clarets still waiting to launch theirs after a second-half goal from Mexico international Raul Jimenez gave the Premier League new boys a deserved victory.
On another tough afternoon, the Clarets were unable to add to their solitary point from the opening day at Southampton as they drew a blank in front of goal for the third time in five games.
Boss Sean Dyche paired Ashley Barnes and Wolves striker Sam Vokes up front for the first time in the Premier League this season - as well as re-calling the fit-again Johan Berg Gudmundsson - to try and take the fight to the hosts.
But it was Wolves who bared their teeth and but for an impressive performance from goalkeeper Joe Hart – and a number of goal-saving interventions from fellow England international James Tarkowski – it could have been a heavier defeat.
Wolves were unchanged for a fifth successive time on the back of the impressive start to their return to top-flight football.
That included draws with Everton and defending champions Manchester City in their first two home games - morale-boosting results if not enough to bring a first Premier League win at Molineux since December 2011 which preceded a slump down to League One.
Portuguese Nuno Espirito Santo masterminded the latest stage of the recovery and a surge to the Championship title last season with a squad packed full of his countrymen and reinforced again with a further spending spree this summer.
And flashes of the flair that have restored the sheen to the ‘Old Gold’ were again in evidence in a first half in which all the chances came Wolves’ way.
But Burnley’s determination to get back to their previously renowned resilience and reliability was also evident - Ben Mee another putting his body on the line to try and protect his goal - as they managed to reach the break scoreless.
Hart was a key man, making two saves of international class, reacting superbly to turn away a cross-shot from Helder Costa with the imposing figure of Willy Boly in his eye-line as the giant defender tried to get a touch and then deny Jimenez.
Again, Hart displayed razor-sharp reflexes to keep out a close-range strike in a remarkable flurry of activity around the Burnley goal which also saw Tarkowski block the follow-up from Jimenez and then clear off the line from Jonny Otto.
Wolves wideman Otto was a constant threat and saw another curling effort headed clear by Tarkowski before Boly volleyed over a minute before half-time as the hosts cranked up the pressure.
A bigger let-off followed a minute into the second half when Phil Bardsley’s under-hit back-pass gave Diogo Jota the chance to tee-up Jimenez for an opportunity he should have taken.
But the on-loan Benfica striker wasn’t going to keep missing and with an hour gone he broke the deadlock to put Wolves 1-0 up, sweeping the ball just inside the far post after Matt Doherty had burst clear to poke the ball into his path.
Dyche had sent on Matej Vydra moments before to try and test Wolves at the other end and the summer signing almost made an immediate impact as the Clarets were only inches away from an equaliser.
Johann Berg Gudmundsson’s free-kick reached Vydra beyond the far post and his angled volley just eluded Cork virtually on the line on the other side of the goal when any touch would have taken it over the line.
The Clarets kept pushing but with the game stretched there were inevitable chances for Wolves to add a second and kill the game on the break as they poured forward in numbers to expose an over-worked back four as Burnley found themselves over-run.
Hart blocked a near-post effort from substitute Adama Traore, Doherty scuffed a shot wide and Tarkowski made another goal-saving block from Leo Bonatini as Wolves somehow failed to add to their lead.
That left the Clarets with a glimmer of hope as Wolves continued to keep missing chances.
But any prospect of snatching an unlikely point – and avoiding a fourth successive Premier League defeat for the first time since May, 2015 – disappeared when Gudmundsson curled a long-range free-kick curled just wide and then mis-cued another half-chance in stoppage time which saw Wolves keeper Rui Patricio employed for about the only time in a one-sided encounter.
Wolves: Patricio, Bennett, Coady, Boly, Doherty, Neves, Joao Moutinho, Otto, Costa (Traore 65), Jimenez (Bonatini 76), Jota (Gibbs-White 87). Substitutes: Ruddy, Saiss, Vinagre, Hause.
Booked: Jota, Neves
Burnley: Hart, Bardsley, Tarkowski, Mee, Taylor, Lennon, Cork, Hendrick (Westwood 79), Gudmundsson, Vokes (Wood 70), Barnes (Vydra 56). Substitutes: Heaton, Lowton, Westwood, Ward, Long.
Booked: Bardsley, Cork, Gudmundsson, Taylor.
Referee: Andre Marriner