McCann condemned Wolves to a third game without a win
Burnley held on to an early lead to boost their play-off hopes and ask further questions of faltering Wolves.
Chris McCann scored in the sixth minute for the home side when he rose to meet Wade Elliott's cross and headed home from close range.
Wolves should have drawn level 10 minutes later but Michael Kightly's corner was met by a bullet header from Christophe Berra which flew wide.
Burnley stood firm to leave Wolves with one win in nine league games.
Burnley manager Owen Coyle:
"They are all vital three points in the Championship but having said that we were fully deserving of the three points.
"From the first whistle we were at them and what we showed is that we have a lot to offer. We came out of the traps very quickly and tried to impose ourselves on the game.
"The clean sheet was a big thing for the lads. To stand up and restrict them to few opportunities was a great credit."
Wolves boss Mick McCarthy:
"We are always disappointed when we lose. The last two away games I have set the team up 4-4-2 and we were being loved for it when we were winning but we are not being loved as much now.
"It is a young squad and I have no doubt they have lost confidence. Sometimes it takes a lucky break to get back on top but you have to earn that luck."
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