Tyrone Fagan almost drew Rugby level on the hour mark but his rising effort from 12-yards out hit the bar.
Harriers boss Steve Burr continued to ring the changes.
Off came Marc Williams, Mike Williams, Storer, Vincent and Marshall for Luke Medley, Mickey Demetriou, Jack Byrne, Robert Thompson-Brown and Michael Briscoe.
Rugby also made several changes, with Steve Evans and Lewis Haycock on for Andy Gundelach and Tyrone Fagan.
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