The hosts are now unbeaten in seven games while improving Stanley have now lost just once in their previous six contests.
Lee Molyneux missed a good early chance for the visitors when he fired straight at Daggers keeper Chris Lewington.
However, Dagenham responded with on-loan forward Ashley Chambers twice testing Lewington's opposite number Marcus Bettinelli.
Peter Murphy then forced Lewington into another smart stop as the scoreline somehow remained goalless at half-time.
Accrington were in charge in the second half as Will Hatfield and Luke Joyce both went close to opening the scoring, while the Daggers almost broke the deadlock when Brian Saah fired wide.
The Daggers made three changes in the second half and pushed hard for a winner in the latter stages. Luke Norris was unlucky when his low drive fizzed just past the post and substitute Sean Shields was next to go close, yet he also smashed a shot wide as the contest finished with both sides recording a clean sheet.