In keeping with an untidy start to the game, Wolves took the lead thanks to a goalkeeping mistake by Brian Jensen, who allowed a shot from Ince to go through his grasp following a knockdown by Carl Cort.
Jensen however redeemed himself by saving well from both Lee Naylor and Cort to keep the deficit to 1-0.
At the other end Burnley were restricted to attempts from long range although both Michael Ricketts and John Spicer went close to an equalizer.
Burnley lack of a threat in the final third of a field was perfectly illustrated early in the second half as Jon Harley's corner fell to Mike Duff, but his volley went well wide of goal.
Postma was finally tested as Chris McCann's pull back was met by a stretching Micah Hyde but was kept out by the Wolves keeper.
The visitors could have secured a more comfortable victory after good work by Cort. Fellow striker Tomasz Frankowski missed the target from 18 yards and is still awaiting his first goal since joining the club from Spanish team Elche.
While this results cements the position of Wolves chasing the play-off pack, for the Clarets it means that a desperate run of form continues, with Steve Cotterill's team having only won once since Boxing Day.