Danny Kedwell took advantage of an error from Daggers keeper Chris Lewington to fire the visitors ahead after seven minutes. Danny Jackman almost doubled the lead when he hit the post directly from a corner.
But Daggers gave themselves a foothold in the game when Billy Bingham volleyed in the equaliser on 22 minutes.
The Gills piled on the pressure in an effort to regain the lead, but Lewington saved from Jo Kuffour and Kedwell had a header blocked on the line by Dominic Green.
Daggers made the brightest start to the second half and Richard Rose’s header forced a finger-tip save from Ross Flitney, while Cristian Montano and Green also tested the Gillingham goalkeeper.
The home side finally made their domination count after 65 minutes when Woodall curled in the winner from just inside the box.