Trailing two-nil, the visitors were handed a lifeline in the 60th minute when referee Dean Mohareb dismissed Kevin McIntyre for a challenge on Josh Scott after the striker had rounded goalkeeper Josh Lillis.
McIntyre appeared to go shoulder to shoulder with his opponent, but a penalty was awarded to the visitors and the Dale defender for a professional foul.
Mickey Spillane scored from the resulting spot-kick and minutes later Dagenham were on level terms when Sam Williams headed home Medy Elito's corner. Dagenham almost won it late on when Danny Green hooked the ball over Lillis but a post spared the hosts from further misery.
Up until McIntyre's dismissal, Rochdale had been controlling the game. Ryan Edwards crashed a shot against the woodwork before Dele Adebola fired them ahead in the 33rd minute with a smart turn and shot from the edge of the area.
Four minutes later Bobby Grant curled another decisive finish past Chris Lewington from a similar position to seemingly put the hosts in firm control.