Hull still attacked briefly despite the three-goal deficit and top scorer Alexander headed a set-piece over on 71 minutes.
But Harriers continued to threaten and Broughton had a good chance soon after only to put the ball into the side netting after tremendous link-up play between all three midfielders.
Alexander headed Beresford's cross over on 82 minutes as Hull again had an opportunity to get themselves on the scoresheet but Harriers, who brought on Foster for Henriksen on 69 minutes and Ducros for Larkin eight minutes from time, continued to play some neat, swift football.
Brock kept his clean sheet intact with a fine diving save from the alert Alexander three minutes from time.
The chances continued to come for Harriers though and Ducros released Broughton only for the big forward to drive wide from the edge of the area.
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