Torquay had wasted a great chance to take the lead when Scott Rendell headed against the inside of a post from six yards in the 14th minute.
Alan Goodall headed straight at Torquay goalkeeper Michael Poke amd Dominic Green also wasted a good chance for the home side before half-time.
Torquay thought they had scored in the 68th minute when Jake Thomson's low shot crept inside the far post but an offside flag cut short the celebrations.
Chesterfield went in front four minutes later when Green broke down the left and crossed low for Conlon to sweep a low shot past Poke from 15 yards.
Tommy Lee kept his side in front with a brilliant reaction save to turn over a Chris Zebroski volley and Nicky Wroe was denied an equaliser by a goalline clearance from Danny Hall.
Source: Team Talk