Another injury-hit Hitchin line-up was defeated by two goals in the last 15 minutes at Rugby's impressive Butlin Road ground.
The Canaries went to Rugby without Josh Sozzo, Gavin Jaggard, Paul Covington and Darran Hay, and gave a debut to new signing Julian Old.
In a poor first half, Hitchin failed to test the Rugby goalkeeper, a deflected shot by Gordon Barr being their only effort.
At the other end, the lively Robbie Beard had three chances, and a good save from Richard Wilmot prevented the Rugby striker from opening the scoring.
Hitchin improved in the second half, and in the 52nd minute, Mark Bridge thought he had given his side the lead only for referee Mr Tierney to rule the effort out. In the Canaries best period, they had two claims for a penalty turned down, first a handball incident and then when Bridge appeared to be brought down.
Rugby regained the initiative and a near-post header by Steve Evans was only just wide, then James Kidd cleared another shot off the line.
In the 75th minute, Rugby took the lead, Beard twisting and turning before sending a well-placed chip beyond Wilmot. And the home side secured the points in the dying seconds when substitute Jon Douglas shot home from close range after being set-up by Justin Marsden.
Hitchin: Wilmot, Barr, Kidd, Burke, McCulloch, Scott, McMenamin (Duffy h/t), Maynard, Bridge (Case 80), Cavill, Old
