Dagenham scored three second-half goals to ensure a winning start to their Conference campaign.
Chris Moore made the breakthrough in shooting low into the bottom corner of the net from the edge of the area.
Glen Southam slid home Dagenham's second goal from close range and Mark Janney fired a fine third, latching onto John Taylor's pass to rifle home.
Stevenage got a consolation goal late on when Jon Brady headed home from close range in stoppage time.
Dag & Red: Roberts, Goodwin, Cole, Uddin, Vickers, Janney, Leberl, Southam, Flynn, Taylor, Moore (Mackail-Smith 87). Subs Not Used: Baruwa, Blackett, Griffiths, Hill.
Goals: Moore 55, Southam 76, Janney 85.
Stevenage: Woodman (Hanlon 45), Gregory, Hocking, Rogers, Quinn (Warner 53), Brady, Bulman, Brough, Boyd, Quailey (Elding 73), Nurse. Subs Not Used: Hodgson, Flack.
Goals: Brady 90.
Ref: P Miller (Bedfordshire).