Ashley Barnes and Chris Wood put the home side ahead before the hour mark before Fabio Silva's first Premier League goal from the penalty spot halved the deficit.
The defeat means Wolves drop into the bottom half of the table ahead of next Sunday's meeting with Tottenham Hotspur.
Tricky evening for back five:
Rui Patricio: 6/10: Controlled his area well and was quick to get down low and deny Barnes, but couldn't do much with the striker's goal.
Like the first goal, Patricio couldn't do much about Wood's goal, as the striker's volley came just as the Portuguese goalkeeper could collect the ball.
Max Kilman: 6/10- Had a quiet game and wasn't at fault for any of the goals. His job was made partially more difficult by the more attacking left wing-back in Ait-Nouri, but he coped well with any balls that came his way.
Conor Coady: 6/10- Like always, Coady's leadership was vocal enough for everyone to hear. He will be disappointed with the goals conceded, but, as the middle man of the back three, the chances were created around him.
Romain Saiss: 5/10- In his first game back in the starting XI, Saiss lost Barnes for Burnley's first real opportunity from the long ball, but recovered well to apply pressure to the Burnley forward.
In the dying moments of the game, Saiss opted to go for goal rather than sending the ball across to Silva in a frustrating performance on his return.
Nelson Semedo: 6.5/10- Despite receiving stick in recent weeks, Semedo's performance certainly impressed at the start of the game with his high runs up the field.
Following Traore's introduction, he saw less of the ball, but he constantly offered himself to help the pacey winger.
Rayan Ait-Nouri: 5/10- The ball struck him for Burnley's second goal, despite not knowing much about it. Like Semedo, his high pressing up the field did help Wolves early on, but it slowly deteriorated.
Battle in the middle won by Burnley:
Joao Moutinho: 5.5/10- After coming back from suspension, Moutinho started well with some dangerous deliveries from sit-pieces. The midfield battle provided a tough one against Ashley Westwood and Josh Brownhill, but Moutinho's experience helped Wolves dominate early on.
Was a very lucky man to not receive a red card at the end of the game after VAR deemed his challenge on Brownhill okay.
Ruben Neves: 6.5/10 Known for his long-range strikes, Neves came close on two occasions at Turf Moor. With Otasowie attacking more, Neves sat deep with Moutinho, looking to pick up any loose balls.
Once two goals down, Neves was forced to push further up and express himself more, but the solid defence of Sean Dyche's men remained resilient.
Owen Otasowie: 6/10- Ventured forward the most between the three midfielders, providing an option for Podence and Neto. Despite being booked, the young American's dynamism seemed to be Wolves' most threatening against Burnley's physical defence.
Lack of a number nine hurts Neto and Podence:
Pedro Neto: 5/10- Unlike in his performance on Tuesday against Chelsea, Neto struggled to impact the game. The young winger's inverted runs did look troubling for the home side, but once they went ahead, he struggled to cope with the low blocks of the defence.
Daniel Podence: 6/10- His natural game of taking the game to the opponents seemed missing on the night. He struggled to compete with the physicality of the Burnley defence, but looked much better once Silva was introduced.
Fabio Silva: 7/10- Winning and converting the penalty will do wonders to his and Wolves' confidence going forward after struggling to find the target beforehand. The game was certainly impacted from his introduction and caused Burnley problems in the air.
His presence inside the penalty area certainly showed and certainly calls the question of whether he should start against Tottenham Hotspur.
Adama Traore: 6/10- Created Wolves' first real opportunity moments after coming on, but was worked out early by Dwight McNeil and Charlie Taylor. He delivered a great ball in injury-time for Saiss, but he ultimately struggled in the pouring rain.