Castle struggled to get their game together and their local rivals were full value for their victory, courtesy of a goal by Dave Walker on the hour.
Walker chased a long ball over the top by Dave Harper and found the net with a half-volley across home keeper Danny Read.
It was no more than Kidsgrove deserved for they only had themselves to blame for not building a commanding lead by half-time.
Liam Shotton fired into the side-netting in the first minute as the visitors made a determined start, and Walker cleared the bar with an overhead kick.
As Kidsgrove dominated the game Paul Donnelly did well to stop Shotton in his tracks, while Read saved one-handed from Ricky Bridge.
Shotton steered another header wide from a deep cross by Tim Sanders, while Newcastle offered little in reply, apart from a couple of efforts by Alan Nagington that failed to trouble Steve Intihar.
Lacklustre Newcastle were little better on the resumption, although Chris Budrys had one effort tipped away, on what was Kidsgrove's night.
NEWCASTLE TOWN: Read, Espley, Skelton, Donnelly, Dicker, Douglas, Johnson, Connor, Budrys, Nagington, Sidibe. Subs: Willis, James, Price, Hughes, Dutton.
KIDSGROVE: Intihar, Smith, Dove, Ward, Harper, Charlton, Urwin, Sanders, Walker, Shotton, Bridge. Subs: Morris, Turner, Schwarz.
Writes the Sentinel