Boden helps Spireites to progress in 'tricky' tie
Harrow goalkeeper Nick Jupp kept the League Two side at bay in the first half, making a number of saves from Spireites pair Scott Boden and Jordan Bowery.
Chesterfield finally broke the deadlock when Boden headed in from Danny Whitaker's well-executed cross.
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Hide AdWhitaker was again the provider when Craig Davies fired home from inside the penalty area deep into stoppage time.
Chesterfield boss John Sheridan said: "Most important thing is that we're into the next round and we've kept a clean sheet.
"For some reason these non-League sides up their game by 50 per cent. I know it would be a tricky game.
"I felt it was important that one or two could get a full game or match practice."
AFC Wimbledon and Ebbsfleet United drew 0-0, and there were no goals in the matches between Barnet and Charlton, Brighton and Woking, Stevenage and MK Dons.