Broughton finally managed to find the target for Harriers on 21 minutes after holding off Kelly but it was a weak effort straqight at keeper Flahavan.
There was a moment of spark from the visitors in a dull game on 23 minutes when Bramble burst past Williams and Hinton on the right but blazed high over the bar from the edge of the area.
There were far too many aimless balls being played but Harriers' Melligan gave some hope with a silky run just after the half-hour mark.
The on-loan Irish midfielder raced from his own half into the Southend penalty box unopposed but blasted off target from 15 yards.
Melligan was again in the action two minutes later, cutting in the from the left before drilling the ball across the face of goal with Southend safe again,
The recalled Broughton should have done better on 35 minutes when Smith, supplied by Morgan, found the front man with a good right-wing cross but he headed wide at the far post.
Soon after Southend made the first substitution of the match with striker Rawle off injured and Marney, signed on loan from Brighton, replacing him.
The substitute immediately made an impact beating Morgan, who had previously made few errors on the left, but Digby advanced to block his low pass across goal for a corner.
Harriers successfully defended the flag-kick, Southend's fourth of the evening, and went into half-time goalless after some poor first half football.
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