The three points lifted John Coleman's side up to 17th place in the League Two table.
However, a 22nd defeat of the season has left the Daggers looking anxiously over their shoulders in the tightening race to avoid relegation from the Football League.
Stanley were on top in the opening stages with Paul Mullin a constant thorn in the side of the Dagenham defence.
But for all the home side's possession, it was the Daggers who forged the first real opportunity when Paul Benson drew a fine save out of Kenny Arthur with a low shot.
The game's decisive moment came two minutes after half-time when Edwards scored his first goal of the season.
The defender rose to meet Ian Craney's corner and left the keeper with no chance as he powerfully headed home.
The goal stung the visitors into life and Shane Huke had a shot cleared off the line, before Benson wasted a gilt-edged opening when he headed over the bar from close range.
Stanley's Leam Richardson was sent off for a second bookable offence in the 89th minute, but by then the home side had done enough to secure all three points.