Enoch Showunmi pounced with three minutes left to nod Peter Holmes' miss-hit volley past Carl Muggleton and maintain Town's four-point lead at the top of the division.
It was no more that the Hatters deserved after a one-sided game in which they missed a string of fine chances.
Muggleton tried to deny Showumni before he was finally beaten and also kept out efforts from Ahmet Brkovic and Calvin Andrew.
In contrast Chesterfield rarely threatened and the closest they came to scoring was when Derek Niven flashed a low drive inches wide.