© PA Photos
All the early chances fell to Burnley, who were having a lot of joy down the left-hand side thanks to Ross Wallace.
He picked out Danny Ings twice inside the opening 20 minutes, but the forward was unable to direct either header into the net.
The visitors took the lead against the run of play in the 21st minute when Curtis Davies was allowed a free header from a corner.
It remained 1-0 to the Blues at the break, but Sean Dyche's men came out rejuvenated following the break.
They were denied an equaliser by Butland's brilliant save from a Sam Vokes header.
However, a penalty given for a foul by Paul Robinson on Stanislas gave Wallace the chance to level, and he duly dispatched the spot kick.
The hosts went down to 10 men with half an hour left to play when Dean Marney was given his marching orders for a late tackle on Robinson.
It was left to King to decide the points, as he found the net from 12 yards out in the last minute.