Carlisle made a half-time substitution as on-loan forward Skinner replaced Halliday.
Harriers threatened early on and Broughton failed to make contact with an inviting Blake cross from the right.
And Carlisle took the lead on 49 minutes when Foran was given a completely free header on the edge of the six yard box and he found the net from Murphy's driven left-wing corner.
It was the first goal veteran keeper Nixon had conceded in the third game of his non-contract spell.
Carlisle nearly made it two on 58 minutes when Soley's sweetly struck 25 yard left-foot volley shaved the outside of Nixon's post.
Clarkson was booked for fouling Murphy on the hour and Morley fired the resulting free kick just off target. Ian Clarkson
Harriers boss Molby responded to the goal by switch to a 4-3-3 formation as Foster replaced Bird on 61 minutes.
A sloppy pass from Williams let in Carlisle on 66 minutes and midfielder McGill eventually drove wide of Nixon's right-hand post.
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