The Poachers slumped to back-to-back defeats for the first time this season.
A horrendous afternoon began badly as the visitors converted a penalty after just 4 minutes.
Debutant Liam Adams came close to equalising when he hit the crossbar – but Heanor dealt another blow to go 2-0 up just before the break.
If Poachers fans expected their side to come roaring back into in the second half, they were in for a shock as the away side grabbed two more quickfire goals before the hour mark.
Town: Woolley, Borbely, Thompson, Ofushine, Ford, Tate, Beeson, Adams, Burdass, Limb, Bayliss; subs: T White, L White, Sylla, Portas
Boston Town FC 