Paul Parry's stoppage time winner gave high-flying Hereford the three points.
Chances were few and far between for both sides before he smashed in an 18-yard volley seconds from full-time.
Parry had gone close in the second minute when his effort was cleared off the line by Richard Scott while Mark Beesley also had a shot scrambled away.
Stevenage's best chance fell to Simon Wormull but he sliced his shot wide with only keeper Matt Baker to beat.
Hereford: Baker, Green, James, Uddin, Craven, Williams, Smith,
Rose, Parry, Beesley, Purdey. Subs: Scott, Brown, Teesdale,
Stevenage: Perez, Brady, Smith, Warner, Gould, Wormull,
Holloway, Scott, Watson, Cook, Maamria. Subs: Shamlian,
Richards, Jenkins, Baptiste, St. Ledger.
Referee: P Melin (Frimley)