Harriers were spurred on by their goal, inparticular midfielder Parrish who sent an angled volley onto the side netting on 72 minutes after collecting Broughton's nod-down.
Hull midfielder Regan was booked on 74 minutes for a foul on McAuley before Williams saved Harriers by nodding Elliott's header off the goal line.
The visitors brought on Foster and Bishop on 78 minutes for Shilton and Parrish but Hull were 3-1 ahead by the 80th minute.
Walter robbed Hinton on the left flank after Elliott's pass forward and ran on to beat the advancing Brock from an angle. Craig Hinton
Hull brought on Russell for Walters on 83 minutes and then Webb for Elliott three minutes from time.
There was further defensive misery for Harriers on 88 minutes when Burgess was left completely unmarked to head a right-wing cross over the stranded Brock and complete his hat-trick.
Harriers defender Hinton was booked in the dying moments for tripping-up Burton.
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