Dan Bentley denied Josh Brownhill and Sander Berge in the first half, but the Clarets remain second bottom while Wolves – who recorded a first clean sheet since August – climb to 12th, 11 points above the relegation zone.
Fresh from their 5-0 thumping of Sheffield United, which ended a seven-game losing run, the Clarets looked to control the game.
But it was Pablo Sarabia who had the first real chance when his deflected strike was tipped over by James Trafford before the midfielder volleyed over.
All of Wolves’ home games this term had come against the top eight – which had seen them beat Manchester City and Tottenham – but against relegation-threatened Burnley there was added expectation.
Yet they struggled to find their fluid best as the visitors bossed first-half possession with Zeki Amdouni testing Bentley from distance.
With growing momentum, the visitors found further confidence and Jacob Bruun Larsen fired over before Bentley bailed Wolves out six minutes before the break.
Joao Gomes lost out to Amdouni and Johann Gudmundsson as he tried to see the ball behind with the latter crossing to Berge. His shot was blocked by Bentley and the goalkeeper then produced a better save to turn Brownhill’s volleyed follow up wide.
But, despite Burnley’s pressing, the soft centre which has now seen them lose 12 of their 15 games cost them again after 42 minutes.
It was sloppy as Trafford and Dara O’Shea played out from the back before Berge’s heavy touch allowed Sarabia to nip in and find Matheus Cunha.
The striker picked out the unmarked Hwang in the area who kept his composure to roll past Trafford.
Kompany’s men only had themselves to blame and could have fallen further behind when Mario Lemina nodded over two minutes into the second half.
The dynamic had shifted and it was now Wolves in the ascendancy with Trafford palming Sarabia’s free-kick away just after the hour.
Burnley were blunt and hardly tested Bentley, although Vitinho drove over from the edge of the box with 13 minutes left, but with their fading threat went their chances of recovery.