A Sam Vokes goal late in the first half looked to have given Burnley a valuable lead, but Chris Maguire's equaliser on 45 minutes levelled the game.
It was the Clarets who had the first chance of the contest when top scorer Danny Ings flicked the ball past Chris Kirkland, only for Keith Treacy's shot to deflect wide of the Wednesday post.
Ings and Vokes linked up well in the opening 45 minutes and it was Vokes's volley past Kirkland which gave the hosts the advantage.
However, just minutes later Maguire's right-footed strike found the back of the net to leave the game delicately poised at 1-1.
A win for Burnley will close to gap on leaders Leicester back to four points.
