In an entertaining contest, the hosts started brightly but the Mariners took the lead through Nathan Clarke, before Sam Jones doubled their advantage before half-time.
Chesterfield poured forward after the break in search of a way back into the game but Town stood up to the pressure well until substitute Kristian Dennis eventually did manage to pull a goal back with eight minutes to go. But Grimsby's response was almost immediate as Ben Davies restored their two-goal cushion from the penalty spot after Harry Cardwell was fouled, to the delight of the 2,650 travelling supporters.
Town: J McKeown, D Collins, P Dixon, N Clarke, Z Mills, S Dembele (B Davies, 75), M Rose, J Berrett, S Kelly (L Summerfield, 55), S Jones (H Cardwell, 79), S Vernon.
Subs not used: B Killip, J Keeble, T Bolarinwa, K Osborne.