Shilton, in good form on the left wing, swung over a good cross on 28 minutes but Broughton could not keep his header on target under pressure from a Hull defender.
There was a scare for the home side on 30 minutes when Branch flashed a cross-shot across the face of Brock's goal.
A good Harriers move five minutes before half-time ended in Henriksen's 18-yard strike being scrambled away by the Hull keeper.
Soon after, Broughton escaped onto an Ayres long ball but Musselwhite turned his low shot wide of the right-hand post.
Harriers striker Broughton was booked for dissent on the stroke of half-time.
Hinton exchanged passes with Melligan and burst into the box in injury-time and his vicious drive was well saved by the busy Musselwhite.
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