Harriers have now gone well over five hours without a goal being scored in one of their matches.
Broughton came close for the visitors on 51 minutes when he drove crisply from 25 yards but the ball just cleared the bar.
Kidderminster cut Shrewsbury open on the right a minute later when Durnin released Skovbjerg but he crossed low into the box before Broughton could arrive at the near post.
Shrewsbury boss Ratcliffe pulled off Jagielka on 62 minutes and replaced him with Wilding.
Durnin blasted a great chance over the bar for Harriers on 64 minutes after he was let in by a terrible error from left-back Drysdale who misjudged Hinton's long pass.
Shrewsbury striker Harris came off on 65 minutes and was replaced by youngster Lowe.
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