Guy Madjo struck twice to secure some vital points for Crawley, who started the season with a six-point deduction for going into administration.
Madjo slotted in from 12 yards on 10 minutes, adding a second with a fierce drive from the edge of the area.
Stevenage pulled one back as John Martin hit a stunning 25-yard strike with 25 minutes left to play.
Madjo was denied his hat-trick when Alan Julian saved from six yards but he had already done enough.
Crawley Town: Bayes, Wilson, Stevens, Ujah (Thomas 33), Bull, Scully (Evans 90), Thompson, Pinault, Cook, Pittman (Vieira 74), Madjo.
Subs Not Used: Judge, Bulman.
Booked: Ujah, Thomas, Madjo.
Goals: Madjo 11, 37.
Stevenage: Julian, Fuller, Arber, Henry, Nutter, Martin, Cole (Dobson 85), Lewis, Miller, Morison, Bramble (Allen 61).
Subs Not Used: Gaia, Russell, Anderson.
Booked: Bramble, Fuller, Morison.
Goals: Martin 66.
Ref: N Kinseley (Essex).