Raul Jimenez netted his 26th goal of the campaign with a sumptuous volley in the 76th minute after substitute Matt Doherty's attempt ricocheted into his path.
Chris Wood missed a sitter from six yards out late on, but the New Zealander made amends in the 96th minute to stretch Burnley's unbeaten home record to seven.
The striker kept his composure to beat Rui Patricio emphatically from the spot, slamming his kick right into the top corner.
Here are the ratings...
. Nick Pope 6
The Burnley is still level with Ederson in the battle for the Golden Glove, despite conceding, but there was little he could do to keep out Jimenez's volley. Wolves had plenty of the ball without really testing Pope.
. Phil Bardsley 5
Struggled when isolated by the impressive Vinagre in the one-v-one and lacked composure on the ball at times, opting to put his foot through it. Failed to cut out Traore's run in the build up to the opening goal.
. James Tarkowski 7
Solid at the back, keeping Jimenez quiet for the most part, and didn't look like conceding until Doherty's strike ricocheted fortuitously into the Mexican's path. Assured on the ball and won his battles.
1. Nick Pope 6
The Burnley is still level with Ederson in the battle for the Golden Glove, despite conceding, but there was little he could do to keep out Jimenez's volley. Wolves had plenty of the ball without really testing Pope.
2. Phil Bardsley 5
Struggled when isolated by the impressive Vinagre in the one-v-one and lacked composure on the ball at times, opting to put his foot through it. Failed to cut out Traore's run in the build up to the opening goal.
3. James Tarkowski 7
Solid at the back, keeping Jimenez quiet for the most part, and didn't look like conceding until Doherty's strike ricocheted fortuitously into the Mexican's path. Assured on the ball and won his battles.
4. Kevin Long 7
Wolves had little joy through the middle as Long, Tarkowski and company protected the edge of their penalty area resolutely. Stuck a boot in when needed, stopping Podence in his tracks in the second half.