Burnley strikers Andy Gray and Robbie Blake combined superbly just two minutes later as Gray blazed a left-foot shot just over the crossbar.
The visitors did have the ball in the net after 14 minutes through McPhee but his effort was correctly ruled offside.
Midway through the first half a game of head tennis in the Burnley penalty area ended with Kiraly saving a left-foot volley from Damien Delaney.
Eight minutes before the break, Kiraly produced another save pushing a shot from Richard Garcia behind for a corner.
Hull goalkeeper Boaz Myhill was called into action six minutes into the second half as he went down to his right to save a shot from Chris McCann.
The Clarets were indebted to another save by Kiraly after 56 minutes with the keeper stopping a Hughes strike.
Burnley almost broke the deadlock on 63 minutes when Graham Alexander's cross was headed against the crossbar by McCann.
The home side were reduced to ten men six minutes from time when central defender David Unsworth was shown a red card by referee Chris Foy for a professional foul on striker Fraizer Campbell. The resultant free-kick from substitute Dean Windass was deflected for a corner.
Both sides created opportunities as they pressed for their three points with Burnley substitute Alan Mahon testing Myhill at one end, whilst at the other, McPhee missed a further opportunity by dragging his shot wide with only Kiraly to beat.
The only goal of the game arrived four minutes in stoppage time as Dean Marney crossed for Turner to head the winner from inside the six-yard box.