Broughton headed over a Clarkson cross on 72 minutes as Harriers searched for a equaliser.
But they seemed to be getting nowhere fast although Blake and Broughton again saw headers drop wide of the goal.
Keeper Keen was at last forced into action to turn away Foster's 18 yard deflected drive on 79 minutes.
Carlisle brought on Allan for McGill on 82 minutes and then replaced Murphy with Jack three minutes later.
Five minutes from time, Foster swung in a promising cross from the right and skipper Blake glanced a header just wide of Keen's right-hand upright.Mark Blake
But Carlisle reminded Harriers of their threat as Allan tested Nixon with a low drive two minutes from time.
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