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...
9. Dwight McNeil 7
Worked hard in and out of possession, doubling up on Traore in an attempt to negate the Spaniard's threat. Provided a valuable outlet for the Clarets to ease some of the pressure and made things happen when switching infield.
10. Jay Rodriguez 6
Didn't effect the game to the extent he has done in recent weeks, but worked hard across the line to close the Wolves defence. Blazed over the bar on the turn before the break before being withdrawn with a suspected knee injury.
11. Chris Wood 6
Wasn't in the game in the first half, looking slightly off the pace, though put himself about a bit more after the break. Missed a sitter late on, but made amends when winning and then converting a penalty deep into stoppage time.
12. Johann Berg Gudmundsson 6
Looked bright following his introduction on the half-hour mark, working tirelessly in both directions. Played a peach of a pass across to Jay Rodriguez in the first half and continued to look creative.