Burnley should have gone in front as early as the third minute but striker Ade Akinbiyi headed a cross from Wade Elliott wide of the target.
Wolves went in front on 13 minutes when striker Sylvan Ebanks-Blake sent Seyi George Olofinjana racing clear to place his shot beyond Kiraly.
The visitors increased their lead just two minutes later as central defender Carlisle underhit his backpass to goalkeeper Kiraly, whose attempted clearance was charged down by Michael Gray with the ball bouncing into an empty net.
Burnley tried to respond to this double setback and from a Robbie Blake corner central defender Stanislav Varga headed wide at the far post.
Wolves goalkeeper Wayne Hennessey made a fine save from Graham Alexander on 32 minutes, pushing a shot from the full-back behind for a corner.
Burnley continued to make life difficult for themselves defensively, as five minutes into the second half Neil Alexander was robbed of possession by Gray, but was rescued by goalkeeper Kiraly who dived bravely at the feet of the Wolves player.
Kiraly then turned villain five minutes later as he allowed a shot from Ebanks-Blake to trickle over the goal-line after the striker had played a one-two with Andy Keogh on the edge of the penalty area.
Olofinjana then slipped a pass to Keogh in behind two Burnley defenders, but the striker dragged his shot wide.
Kyle Lafferty went close to pulling a goal back but his shot from 20 yards flew just wide of the target.
The home side did manage to get on the scoresheet 14 minutes from time, when Akinbiyi scored at the second time of asking after his initial effort had been parried by Hennessey.
The result boosts the hopes of Wolves making the play-offs, while the scoreline was a major blow to Burnley's hopes of being involved in the end of season shake-up.