Castle took 18 minutes to get off the mark when, following a long ball by Ryan Dicker, striker Alan Nagington fired past keeper Steve Intihar.
Grove replied when Matt Haddrell (pictured) steered a header over the bar from 12 yards after Tom Urwin had cut the ball back from the byline. But on 34 minutes Castle doubled their lead.
Peter Heler did the spadework in getting the ball into Chris Budrys, whose half-volley went in off Intihar at the near post.
Kidsgrove enjoyed their share of possession without creating more than half-chances.
And Castle made an ideal start to the second half by adding their third on 52 minutes when Dicker headed home Jordan Johnson's corner.
John Sheldon had a free-kick tipped over by Intihar, while home keeper Danny Read was never troubled throughout the game, writes the Sentinel.