The home side competed well up until half-time, but faded badly after the break and three goals in the space of 28 minutes made sure the visitors secured the points.
Goals from Tim Cole, Danny Foster and Chris Moore were enough for Dagenham to celebrate, while Rovers are left to contemplate what promises to be a nerve-racking finish to the season.
The deadlock was broken in the 62nd minute when Cole headed home from a Sam Saunders cross.
Eight minutes later it got even better for the visitors as they doubled their advantage when a Foster header left Rovers goalkeeper Ryan Clarke well beaten.
And to rub salt into an already gaping wound, Moore netted in injury-time with a sweet left-foot strike.
Earlier Dagenham almost opened the scoring through Cliff Akurang, but his header was saved by Clarke.
Paul Wanless and Darren Jones went close for the home side, before Wanless fired over and Craig Dove had a shot saved by Dagenham keeper Tony Roberts.
Saunders fired wide for Dagenham, while Rovers' Abdou Sall saw a header saved three minutes before the break.
But the resumption saw Rovers struggle to find their feet and Dagenham were worthy winners as they cemented their place in mid-table.