Harriers were looking comfortable with their one goal lead although they survived a minor scare on 67 minutes when a Tudor back header drifted wide of the post. Ian Foster came on as a substitute late on
Seconds later, Parrish came on for Williams in his first league appearance since early September.
Cambridge, who earlier replaced Youngs with Nacca, then made their second substitution on 70 minutes with striker Chillingworth on for full-back Jordan.
Cambridge won a dangerous free kick on 76 minutes after a foul by Bennett but substitute Chillingworth struck the 25-yard set piece straight into Brock's hands.
Harriers made their second switch on 79 minutes with a straight swap as Foster replaced Henriksen.
And only the crossbar denied Foster three minutes later from his right-wing cross-shot after Broughton had held the ball up well.
From a Cambridge corner Tann put a header straight at the keeper.
And Cambridge were only denied in injury time by an excellent full-length save by Brock to turn Goodhind's header round the post from a Tudor corner.
Kitson as booked late on for Cambridge after catching Ayres in a challenge with his elbow.
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