Zavon Hines and Rhys Murphy struck once each in five second-half minutes to condemn James Beattie's side to their eighth defeat in 10 league matches, despite substitute James Gray's injury-time consolation.
Stanley are now four points from safety, having played a game more than their fellow strugglers, while their visitors are up to eighth, just two points shy of an automatic promotion spot.
Wayne Burnett's men have lost only twice in the league this season and they fully deserved the three points at the Crown Ground.
On-loan Fulham goalkeeper Marcus Bettinelli kept Accrington in the contest in the first half, but he had no answer to the visitors' quick-fire double after the interval.
Hines netted the first from inside the box with 55 minutes on the clock and, with Stanley still reeling, he turned provider as Murphy doubled Dagenham's advantage.
Gray left it late to reduce the deficit, having been introduced in the 73rd minute, but his second goal of the season could not stir a comeback.
