The Grecians went two goals in front through their potent strike pairing of Jamie Cureton and Richard Logan.
Cureton got the first on 18 minutes when he turned in a Steve Tully cross from close range and Logan doubled Exeter's lead on 32 minutes when he skilfully flicked the ball in at the near post from Scott Golbourne's centre.
County pulled themselves back into the contest with a goal on the stroke of half-time.
Ben Davies' free-kick was met by Lee Hughes who powered a header past Artur Krysiak in the Exeter goal.
But it was Ryan Harley who got the third goal for Exeter in the 66th minute when he raced from halfway and took his time before planting a fine low shot across goal and in off the far post.
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