Hull threatened first in the second half when Elliott crossed from the left for Branch to head over at the far post on 52 minutes.
A Henriksen header was blocked by defender Anderson a minute later and then Harriers defender Stamps was booked for fouling Jevons.
The home side took the lead on the hour with a goal from Henriksen who rifled home a 15-yard finish from Hinton's cross.
Harriers kept attacking and only the head of Ashbee prevented a Broughton lob from making it 2-0 on 63 minutes.
A lapse in concentration at the other end allowed Branch to nip in on 67 minutes but his header cleared the bar.
Hull made their second substitution on 64 minutes with Dudfield on for Elliott.
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