The home side were brimming with confidence after last week's Cup victory against Leyton Orient and midfielder Glen Southam unsettled the visitors defence with a clever run and shot in the tenth minute.
Stanley weathered the storm and almost hit Daggers with a sucker-punch 60 seconds later when David Brown fired straight at keeper Tony Roberts from ten yards after latching on to a Leighton McGivern throughball.
The visitors piled on the pressure and it told in the 16th minute when McGivern rose highest in the Dagenham box to power a bullet header past Roberts from Paul Mullin's cross.
Daggers threw men forward in search of an equaliser and hit back in the 26th minute when Danny Foster's strike was deflected in off Stanley skipper Peter Cavanagh.
Cavanagh made amends for his mistake a minute later when he delivered a perfect cross for Andrew Proctor to head the visitors back into the lead from the edge of the Daggers box.
Dagenham boss John Still brought on striker Paul Benson in the 64th minute and last season's top scorer had an immediate impact setting up Foster to cross for Ben Strevens to head inches wide from six yards.
Stanley unlocked the Daggers back-line in the 70th minute when Brown lashed on to a clever Leam Richardson throughball only to shoot weakly at Roberts from six yards.
The visitors bagged the points in the 78th minute when substitute striker Roscoe D'Sane forced a fine save out of Roberts only for Mullin to head home the rebound.
D'Sane came close to making it 4-1 when he fired inches wide after pouncing on a loose ball in the Dagenham box.
The former AFC Wimbledon striker should have done better two minutes later when he headed just over the bar from ten yards with the keeper stranded.
Proctor almost added insult to injury in the last minute when his ambitious 30-yard strike flew wide of Roberts' goal but by then the game was won.