Good handling from keeper Brock denied Wrexham a third goal from a close-range Lawrence header though the lanky defender should have done better.
Hinton became the third Harriers booking on 74 minutes for a foul on Green.
Harriers did not look like scoring though McAuley, who replaced Bishop on 74 minutes, and Flynn tried their luck from distance but both shot wide.
Harriers were denied a consolation in injury time when Parrish's point-blank header was well saved by Dibble following a long Stamps cross from the left.
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