The South Korean scored his eighth league goal of the season, with Gary O'Neil's side now unbeaten in their last five Premier League home matches.
How the match unfolded
Those saves proved crucial as Burnley, who lost Luca Koleosho to injury, fell behind three minutes before the break.
Wolves went closest to scoring in the second half, but Pablo Sarabia’s free-kick and Cunha’s effort from distance were both comfortably saved by James Trafford, while no one was able to connect with Craig Dawson's pass that flashed across goal.
Burnley failed to register a shot on target in the second half and have now lost eight of their nine away matches this season - the worst record of any side in the competition.
Wolves move up to 12th with 18 points, while Burnley remain 19th on seven points.
Next five Premier League fixtures
Did you know?
Wolves have lost just two of their last 12 Premier League games at Molineux, winning seven and drawing three.
Burnley, with seven points, are only the eighth side in Premier League history to accrue seven or fewer points from the first 15 games of a campaign, with all previous seven relegated at the end of the season.
Only Erling Haaland (14) Mohamed Salah (10) and Son Heung-min (9) have scored more goals in the Premier League this season than Wolves attacker Hwang Hee-chan (8).
Matheus Cunha has been directly involved in a goal in each of his last four appearances (2 goals, 2 assists), just one fewer than he managed in his 28 games in the competition before that (4 goals, 1 assist).