Rochdale had already gone close through Jamie Allen's long-range shot before Dagenham fired themselves in front after nine minutes. Medy Elito teed up Rhys Murphy and he drilled home his eight goal of the season, right-footed from just inside the box.
Rochdale bossed the remainder of the first-half, but just could not score.
Peter Vincenti headed a glorious opportunity wide, while George Donnelly's shot on the turn fizzed inches past the post.
The Daggers then extended their lead with a cracking goal seven minutes after the restart. Goalkeeper Chris Lewington's long clearance found Elito and he steadied himself before crashing a shot into the top corner from just outside the box.
The visitors then grabbed a scruffy goal in the 64th minute when Allen's low cross was not cleared and Gary Dicker raced on to bundle the ball home from close-range.
Elito's second goal in stoppage-time from the edge of the box wrapped up a superb victory for Dagenham.