The victory means Grantham finish sixth in the league to set up a play-off at Nantwich Town on Tuesday night.
CLICK HERE to see the Unibond League Division One South table.The Gingerbreads went into the crunch game knowing that a single point would be enough, following Colwyn Bay and Belper Town's 2-2 draw on Thursday night.
Town enjoyed a brief good opening spell with slick passing moves and, camped in the Kidsgrove 18yd box, a goal looked to be on the horizon.
But slack defending at the other end gifted Kidsgrove the lead.
Following good work by Aiden Matranga and Michael Lennon, Ryan Baker fired in from close range.
Shocked by the goal, Grantham's flowing football disintegrated and poor ball control and sloppy defending made for some nerve-jangling moments.
Jason Turner fired a shot over from close range on the half-hour mark and two minutes later Glen Atkinson's effort forced Kidsgrove keeper James Coates to tip the ball over.
As the first half petered out, Town seemed to lack urgency as Kidsgrove displayed increasing confidence.
Phil Hadland and Liam Shotton went close for Kidsgrove shortly after the break and Town skipper Brendan McDaid's 50th minute drive curled just wide.
Town had further chances from Turner, McDaid and 60th-minute substitute Sean Cann before The Meres crowd really came to life in the 66th minute.
The Gingerbreads got their reward from McDaid who dribbled in, following a good ball supplied by Turner, to bring his side level.
Five minutes later, Cann danced into the Kidsgrove 18yd box and chipped just over the bar, bringing gasps from the re-animated Town fans.
And it was Cann who found the winner in the 81st minute.
After dribbling into the box, his initial shot was blocked by a defender but the rebound came back to him and he stepped to the left and placed his shot into the bottom left-hand corner.
Ziccardi was forced to save an 84th-minute Lennon shot but from then on Grantham generally dominated as Kidsgrove appeared to have lost all their fight.
A speculative Sam Mullarkey injury-time cross-cum-shot skimmed the bar before referee Mr Guest's final whistle signalled celebrations from Town's players and supporters.
Grantham Town: Ziccardi, Fleming, Revill, McDaid, Gowshall, Dixon, Minett, Atkinson, Mullarkey, Turner, Norris.
Subs: Gilbert (for Gowshall, 45), Cann (for Atkinson, 60), Lowman (for Norris, 89).
Att: 304
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