Rovers made a strong start and Matt Harrold volleyed against the crossbar after three minutes, following good work from Mustapha Carayol. But the Daggers moved in front after 24 minutes when Josh Parker picked Woodall out with a right-wing cross and the striker volleyed in at the near post.
Carayol and Elliot Richards both had long-range efforts saved comfortably by Chris Lewington before half-time.
In the 54th minute, however, Woodall scored his and the Daggers' second after latching onto a long ball forwards from Luke Howell and volleying in from the edge of the box.
Rovers' day got worse after 64 minutes when substitute Danny Green dribbled through the defence and finished low past debutant keeper Conor Gough.
And Woodall put the icing on the cake with his 13th of the season and third goal of the game, with a fierce low drive to turn in Medy Elito's pass.