Stevenage overcame struggling Stafford thanks a headed brace from striker Steve Morison.
Morison put Borough ahead after just nine minutes when he headed Daryl McMahon's pass beyond Stafford goalkeeper Danny Alcock.
Stevenage made it 2-0 when Morison again beat Alcock with a close-range header from a Craig Dobson corner.
Jemiah Richards steered home Matthew Hazley's free-kick to give Stafford hope, but the visitors held on.
Stafford Rangers: Alcock, Sangare (Street 20), Daniel, Richards, Lynch, Ingram, Draper, Mawene (Jarrett 59), Hazley (Olaoye 75), Grayson, McNiven.
Subs Not Used: Arnolin, Allen.
Goals: Richards 51.
Stevenage: Julian, Fuller, Oliver, Arber, Laird, Dobson, McMahon (Stokes 81), Stuart Lewis, Junior Lewis, Berry (Burke 68), Morison.
Subs Not Used: Russell, Henry, Westwood.
Booked: Stuart Lewis.
Goals: Morison 9, 41.
Ref: J Waugh (West Yorkshire).