John-Joe O'Toole headed in a Lee Brown cross following a short corner after seven minutes to put the home side in front. It was the midfielder's 15th goal of the campaign.
But the Daggers looked slick going forward and equalised midway through the first half when stAzeez found room to nod in a Medy Elito corner.
The skilful forward grabbed the winner in the 58th minute, shooting high into the roof of the net after a Luke Norris pass had put him through.
Azeez had earlier forced a fine first-half save from Steve Mildenhall after a clever turn inside the box, while Rovers went close through a David Clarkson free-kick which was well saved by Chris Lewington.
Kaid Mohamed headed just wide for the hosts from another Brown cross just before the interval.
The second half brought chances for both teams, with Norris firing over and substitute Steven Gillespie shooting narrowly wide for Rovers.