It took some time for the action to heat up on a chilly winter’s night in the West Midlands, but the Clarets were starting to probe a little through blocked efforts from Josh Brownhill and Luca Koleosho.
This seemed to prompt Gary O’Neil’s side into action, with James Trafford forced to tip Pablo Sarabia’s deflected drive over the bar.
The Spaniard came close again moments later after meeting Nélson Semedo’s enticing cross, but his first-time effort flew over the bar.
The Clarets were dealt a blow when the lively Koleosho was forced off with a knock, and Johann Berg Gudmundsson entered the fray.
He almost had an immediate impact after teeing up Jay Rodriguez, whose strike was saved by Dan Bentley, before the Wolves keeper made an even better stop to parry away Brownhill’s strike from the loose ball.
However, Kompany’s men were dealt another cruel lesson about life back in top-flight, after some defensive dithering from Dara O'Shea and Sander Berge allowed Matheus Cunha to tee up Hwang, who clinically broke the deadlock in the 42nd minute.
O’Neil’s side were on top after the break and came close to doubling their advantage when Mario Lemina headed over from Sarabia’s free-kick.
The former Paris Saint-Germain man was one of the key protagonists for the hosts, and Trafford palmed away another one of the Spaniard’s set pieces to safety.
As the game entered the final 15 minutes, the Lancastrians were sensing an opportunity, with Vitinho not far away from restoring parity through a speculative long-range shot.
Despite a spirited end to this contest, it was yet another defeat on the road for a Burnley side that has lost each of their last four away games in the league.
Their emphatic 5-0 win over Sheffield United already feels like a distant memory, in contrast to what will undoubtedly be a feeling of relief for Wolves.
The Black Country club avoided losing three consecutive top-flight matches for the first time since October 2022, ending a run of seven league games without a clean sheet at Molineux.