Jay O'Shea opened the scoring before Marc Richards struck twice to give the Spireites their first victory of 2013.
O'Shea celebrated his first game since he signed an 18-month deal at the club by firing in from 10 yards after he and Danny Whitaker had sliced open the Northampton defence in the 18th minute.
The visitors cracked again a minute later when a dreadful mistake by Clarke Carlisle allowed Richards in to drive a low shot past goalkeeper Lee Nicholls, who was beaten again in the 25th minute when Tendayi Darikwa sent Richards clear to slot in the third.
Nicholls saved from Craig Clay as Chesterfield continued to find holes in the Cobblers' defence, although Northampton wasted a chance to narrow the gap when Clive Platt dragged a shot wide in the 65th minute.
Chris Hackett hit the Chesterfield woodwork six minutes later and Kelvin Langmead had a shot blocked on the line but the damage was done in the first half.