Connor Lemonheigh-Evans gave the Gulls the lead on 11 minutes and Billy Waters added another with 15 minutes remaining.
George Carline and Adi Yussuf both had chances cleared off the line for Town.
The Spireites have now won just one of their last seven and have dropped out of the play-offs with five games to go.
They race Woking away on Saturday next.
Here are Liam Norcliffe’s player ratings from yesterday’s defeat...
The Spireites have now won just one of their last seven and have dropped out of the play-offs with five games to go.
5. Laurence Maguire 6
A whole-hearted, determined performance. Left everything out there. Not seen a replay but could he have done better for Torquay's opener? Photo: Andrew Roe/AHPIX LTD
6. Alex Whittle 5
Recalled to the side in place of Taylor but he looked a bit rusty and appeared to be lacking confidence. Offered little going forwards. Photo: Rachel Atkins
7. Manny Oyeleke 6
He did okay. Can't fault his work-rate. Spreaded play nicely but doesn't look like a player who will play a killer pass. Not yet anyway. Fair play to him for completing the full 90 minutes for the second time in less than 48 hours. Photo: Craig Brough/AHPIX LTD
8. Martin Smith 6
I thought he had a good first-half, he drove forward with the ball from midfield and played forward passes. But he struggled to get going after the break and was taken off with 10 minutes to go. Would have got a higher score had he continued his performance levels in the second 45. Photo: Andrew Roe/AHPIX LTD