Defender Peter Murphy scored a late equaliser to help Accrington continue their solid start to the season.
Dagenham & Redbridge soaked up early pressure before midfielder Luke Howell gave them the lead on the hour mark with a close-range finish.
However, with five minutes to go, Murphy latched on to a Lee Molyneux pass to level the scores.
There was still time for Daggers substitute Danny Green to head wide in injury time.
VIEW FROM THE DRESSING ROOM
Accrington Stanley manager Paul Cook told BBC Radio Lancashire:
"We didn't play well. We never got going and Dagenham made it really difficult for us.
"Going into the second half, they were very much in the ascendancy and a goal for the home team was very much on the cards.
"Once they scored, it ignited us into our best passage of play and we created two or three really good situations.
"The lads have got great tenacity. It's a great compliment that they can keep going, but we had a little bit of luck. Every game you pick up in this league is very important."