Rovers should have taken a lead after just eight minutes when a pass back was only half cleared by Dagenham keeper Paul Gothard. Neil Grayson lobbed the ball back across the face of goal only for Steve Cowe to put the ball the wrong side of the post.
They did take the lead just before the half hour, when a corner was just missed by the incoming Jon Richardson. Alex Meechan played the ball back into the danger area and despite Grayson's header being blocked, the ball was adjudged to have crossed the line.
The lead was increased five minutes before the interval when Gary Owers' deep left-hand cross found the head of Kayode Odejayi, but his header rebounded off the right-hand post and Alex Sykes' belting low cross across the face of goal led to Richardson to knock the ball in from close range.
But the visitors pulled one back in the first half injury time, when a mis-kick by Steve Jenkins allowed Steve West the opportunity to roll the ball beyond Steve Perrin into the right corner of the net.
Less than 30 seconds into the second half, again poor defending by Forest Green allowed Paul Terry, completed unmarked, to tap a right-wing cross into the left corner of the net.
Despite losing their two-goal advantage, Rovers looked to retake the lead and were rewarded after 55 minutes when Odejayi got past his marker and ran clean through. His shot was smothered by Gothard but Grayson was on hand to fire the rebound into the net.
Just three minutes later, the two-goal advantage was restored when Grayson this time set up Odejayi with the Nigerian running through from the halfway line before stabbing the ball through the legs of Gothard.
Just after the hour, the victory was complete when Odejayi's run down the right wing and cross was deflected by a Dagenham defender as far as Cowe, who fired the loose ball into the roof of the net.