Sean McConville nearly gave the visitors a half-time lead, but his firm header cannoned off the crossbar.
With just seven minutes to play, Billy Kee fired home from close range after his first effort was blocked by Dom Hyam to put Stanley ahead.
Dagenham pushed for an equaliser, but Accrington comfortably held on to secure all three points.
The result meant the Daggers are now nine points from safety, while Stanley sit comfortably in fifth place, seven points clear of Wycombe, in eighth.
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Dagenham manager John Still told BBC Radio London: "The boys have competed, as they have done, against a side that's going for the play-offs.
"At the end of the day it's always about the same things. It's about the two boxes; we should have been 1-0 up at half-time.
"Our confidence isn't high but we've competed brilliantly."
Accrington strengthened their position in the play-off places with a hard-fought win over struggling Dagenham.