As so often this season Argyle top scorer Reuben Reid was the home side's hero.
Reid fired the hosts ahead in the 28th minute, sending an angled drive from the right past diving goalkeeper Tommy Lee and in off the far post.
Chesterfield responded with Ritchie Humphreys' 57th-minute strike from the left side of the area that deflected off Argyle midfielder Andres Gurrieri to send it past home keeper Jake Cole.
Reid restored Argyle's lead with a brilliant solo goal two minutes later, skipping between four defenders on the edge of the penalty area before rifling a 20-yard rising shot into the net.
It was Reid's 14th league goal of a productive season and his 18th in total this term.
Chesterfield centre forward Marc Richards went close for the visitors when he smashed a first-time strike off the underside of the crossbar.