Liam Hatch's two-goal contribution swung the first leg in Darlington's favour, although the 28-year-old hobbled off late in the second half to be replaced by Tommy Wright.
Stevenage could have levelled through Charlie MacDonald but Paul Wilkerson produced a fantastic save, and Gravesend squandered two good chances when Bentley shot wide and LiamHatch had a fierce shot blocked by Jamie Campbell.