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...

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Chesterfield were beaten 2-0 at home to Torquay on Monday. Pictured: Liam Mandeville. Photo: Andrew Roe/AHPIX LTD

. Grant Smith 6
Had no chance with the first goal. Might be a little disappointed with Torquay's second, he got a hand to it but it was well-struck and was in the bottom corner. Conditions didn't help him. Did not have much else to do. Photo: Dean Atkins

. George Carline 6
Steady performance. Had a header cleared off the line in the first-half. Photo: Andrew Roe/AHPIX LTD

. Fraser Kerr 6
Not at his best defensively in the first-half, Rowe could be heard shouting for him to get tighter and to be quicker to the ball. One overlapping run and cross almost resulted in an equaliser. Photo: Craig Brough/AHPIX LTD

1. Grant Smith 6
Had no chance with the first goal. Might be a little disappointed with Torquay's second, he got a hand to it but it was well-struck and was in the bottom corner. Conditions didn't help him. Did not have much else to do. Photo: Dean Atkins

2. George Carline 6
Steady performance. Had a header cleared off the line in the first-half. Photo: Andrew Roe/AHPIX LTD

3. Fraser Kerr 6
Not at his best defensively in the first-half, Rowe could be heard shouting for him to get tighter and to be quicker to the ball. One overlapping run and cross almost resulted in an equaliser. Photo: Craig Brough/AHPIX LTD

4. Gavin Gunning 7
Town missed him against Hartlepool so it was good to see him back. He is not fully fit but he is giving everything to be out there. He put in a good display. Photo: Craig Brough/AHPIX LTD