Law gave debuts to three members of the club's Scholarship with four teenagers in the starting eleven.
Debutant Shahriq Ajmal was the pick of the new players terrorising Grove left back Ryan Brown with some mesmerising runs while defender George Dixon kept veteran striker Dave Walker quiet for much of the game.
Desire their dominance, Chasetown's best chances fell to Cameron Stuart from long range while Jono Gould forced Joe Hemmings into a low save.
Kidsgrove caught Chasetown on the break at the start of the second half with Matt Bell turning the ball home following a flowing move.
Hemmings saved well from Nick Turton at his near post and then Warren Holmes bravely blocked a drive from Jelson Antonio.
Kidsgrove doubled their lead through substitute William Booth and the visitors saw out the game with ten men after Stuart saw red for two yellow cards.
Chasetown: Bateman, Smith, Haynes, Turton,, Dixon, Teesdale (Beckett, 38 mins), Ajmal, M Brown, Stuart, Gould (Singh, 60 mins), Antonio.
Other subs: Birt, Grayson, Griffiths (not used)
Only authorised club members can view team selection.
# | Team | Pl | Pts |
11. | Norton United | 42 | 61 |
12. | Romulus | 42 | 61 |
13. | Chasetown | 42 | 51 |
14. | Loughborough Dynamo | 42 | 48 |
15. | Sheffield FC | 42 | 48 |
16. | Goole AFC | 42 | 46 |
17. | Stocksbridge Park Steels | 42 | 41 |