Thorpe opened the scoring on 53 minutes when a corner was headed goalwards by captain John Mackie and the striker was on hand to hit home from six yards out.
Both sides had had chances before that to take the lead, the visitors' first opportunity coming in the 14th minute when Glenn Poole skipped over the challenge of Paul Butler and was clean through, only to be denied by a fine save from keeper John Danby who also blocked Thorpe's follow-up shot.
The visitors could count themselves extremely unfortunate on 27 minutes when Poole left fly with a shot from 25 yards which beat the keeper but smacked against the crossbar.
On 35 minutes it was Chester's turn to rue their luck as Simon Yeo's shot deflected off Adrian Pettigrew and looped goalwards but struck the outside of the post.
Kevin Ellison wasted a good opportunity when keeper Simon Brown came out of his area to head the ball clear, but only found the City winger who snatched at his shot when the keeper was well off his line.
A stumble by Adrian Pettigrew allowed Simon Yeo a run through on goal before the break, but Brown was equal to the task beating the ball away while Yeo lost his footing as he looked to crack in a rebound.
John Murphy also should have done better with a close-range header that went straight at the keeper.
Murphy was again wasteful with another header midway though the second half which went wide of the target, and in the last minute it was left to Moore to race onto a throughball and slide his shot past Danby to seal the points.