A moment of magic from new Chester signing Daryl Clare proved enough to separate these two teams in what was a hard fought but disappointing clash.
The goal which has know consigned Stevenage to their fifth successive home defeat in the league saw the Hertfordshire side slip to second from bottom in the Conference.
But it was rough justice on a Boro team who dominated the opening exchanges and which piled on the pressure at the death with out finding the end product.
Stevenage began with a flurry and the omens looked good when after just two minutes Robin Trott rose to head a corner on to the top of the bar.
Kirk Jackson came close with a half-volley which flew just over while on 18 minutes Richard Pacquette rose to meet a long Jude Stirling throw, but saw his header well saved by Chester keeper Wayne Brown.
Chester had few chances, but Scott Guyett came closest with a header on 22 minutes which was cleared for a corner before the visitors made the break through just before the interval.
Clare, Chester's deadly new signing, found himself free on goal after a neat throughball from Ryan Sugden and he made no mistake as he took the ball forward and drilled past Mark Westhead in the home goal.
It was a strike which the home side barely deserved to concede and although they piled on the pressure in the second half they created few clear cut chances to grab the vital equaliser.
Both Louis Riddle and Michael Blackwood saw shots saved as Stevenage tried to find a way back into the game and even the double substitution, which saw Jean Michel Sigere and Jack Midson come on, failed to knock Chester out of their stride as the title-chasers defended in depth to claim the three points