Raul Jimenez's goal was enough for Wolves to earn their first Premier League home win of the season.
The 1-0 scoreline flattered Burnley, who remained in the game through the brilliance of Joe Hart, with the goalkeeper denying Helder Costa, Jimenez, Otto and Ruben Neves before he was finally beaten after 61 minutes.
Jimenez, who also scored in the draw with Everton during the opening game of the season, got his second goal of the campaign with a deft flick from a Matt Doherty cross.
Burnley, meanwhile, remain without a win in 11 matches in all competitions this season, after their Europa League exploits. They have lost their last four Premier League games - the last time that happened the Clarets were relegated from the top flight, finishing bottom of the table in 2015.
Wolves enjoyed a good spell of early pressure which included four corners, the second of which was well worked to Costa and his cross required a save from Hart, who had to push away the ball after Costa's cross evaded everyone in the penalty area and looked like creeping inside the far post.
Burnley survived and gradually worked their way into the game. They were seeing more of the ball, although the possession was primarily in their own half or the middle of the pitch and, a tame Ashley Barnes effort aside, Wolves goalkeeper Rui Patricio was unworked during the whole match.
The visitors somehow emerged unscathed from another wave of Wolves attacks just after the hour mark. Diogo Jota got to the byline and cut the ball back for Jimenez but Hart did well to save with his feet at point-blank range before Jimenez then saw his header on the rebound cleared off the line by James Tarkowski.
Wolves kept the attack alive and Otto then saw his effort kept out by a combination of Hart and Tarkowski on the goal line before the Burnley goalkeeper finally smothered the ball.
Willy Boly was next to be frustrated as he sent a header narrowly over the crossbar as half-time approached.
There was another let-off for Burnley right at the start of the second half. Phil Bardsley under-hit his pass back to Hart and Jota seized on the loose ball. He set up Jimenez but the Mexico international scooped his shot over the crossbar with only Hart to beat.
Wolves appealed for a penalty after 54 minutes when Jota ran into Tarkowski but referee Andre Marriner saw no foul. Hart was then called upon once more to parry Neves' long-range strike round the post.
However, Hart was finally beaten and Wolves made the breakthrough. Doherty did well down the right and his low cross was directed into the net off the post by Jimenez's first-time flick.
Burnley would have got a quick equaliser had Jack Cork been able to stretch enough to get a touch on a deep free-kick from Matej Vydra at the far post.
Back at the other end, Adama Traore became the latest player to be denied by Hart after he worked a one-two with Jimenez and saw his shot saved at the near post.
It is successive wins in the Premier League for Wolves but the number of chances they miss is becoming a theme this season and that will be a concern for head coach Nuno Espirito Santo.