Ben Strevens and David Rainford struck in the final 15 minutes to give Dagenham a win which takes them closer to the Conference title.
The game had looked to be heading for a stalemate until Strevens fired home from inside the area on 76 minutes.
And the win was sealed three minutes from time when Rainford met Paolo Vernazza's corner on the volley.
Luke Oliver headed over with Borough's best chance as Daggers moved 12 points clear at the top of the table.
Dag & Red: Roberts, Foster , Griffiths, Boardman (Vernazza 24), Uddin, Leberl, Southam, Rainford, Benson, Strevens, Moore.
Subs Not Used: Eyre, Sloma, Saunders, Wallis.
Booked: Strevens, Benson, Moore.
Goals: Strevens 76, Rainford 87.
Stevenage: Julian, Fuller, Nutter, Oliver, Henry, Nurse (Hakim 60), Cole, McMahon (Dobson 62), Beard, Hughes, Morison.
Subs Not Used: Potter, Binns, Deen.
Ref: R East (Wiltshire).