An exciting run from Hull winger Elliott on 32 minutes nearly brought a second goal for the home side but he dragged the ball well wide after bursting past Williams and Hinton.
Shilton, who had earlier put in several useful crosses, then tested keeper Fettif with a good 20 yard shot which the former York man had to tip over the bar on 35 minutes.
Harriers fine spell continued when Henriksen was only denied by an off-side flag after meeting Hinton's cross with a perfect glancing header. Dion Scott
But Hull were gifted a second goal on 38 minutes when Scott failed to clear the ball 10 yards from goal and Burgess poached his second by stealing in to prod home past a despairing Brock.
The Harriers keeper did well to tip a Walters' shot wide on 40 minutes.
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