Harriers forward Broughton connected with another header on 67 minutes, sending the ball looping over the bar from Flynn's long right-wing cross.
Melligan was then given a good opportunity by Williams but probably shot too early from an angle just inside the area with the ball flying over the woodwork.
Southend loan signing from Spurs Kelly was booked afterwards for fouling Williams during the move.
The visitors brought on midfielder Thurgood for J Smith on 76 minutes but Harriers were ahead moment later.
Broughton's flick-on fell for Melligan who nudged the ball past an opponent and lobbed it sweetly over the advancing keeper.
At the other end experienced keeper Digby had to have his wits about him, straight after with a fine low save at his post to deny Marney from 25 yards.
Melligan came close again 10 minutes from time with a flicked header from Flynn's free-kick which Flahavan saved well down to his left.
The Essex side, now searching hard for an en equaliser, made their final substitution on 82 minutes with Jenkins on for Clark.
Harriers then responded with a triple change two minutes later with Parrish, Coleman and Bishop, replacing Henriksen, Adie Smith and Shilton.
But the visitors were busy searching for a crucial goal in front of a crowd of 2,006 - the lowest the league at Aggborough this season.
A stunning 30-yard volley from top scorer Bramble was helped around the post by Digby on 86 minutes and the keeper was then helped by one of his substitutes.
Parrish was on the line to knock the ball away from a towering Cort header following a corner and Marney hooked the rebound wastefully over the bar.
Harriers shot down to the other end and Melligan's edge-of-area drive was superbly tipped over by an outstretched Flahavan.
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