The defender headed home two minutes after the interval, getting on the end of an Ian Craney corner.
Stanley forced the early pace with Paul Mullin their main threat in a first half which lacked goalmouth action.
Daggers striker Paul Benson did force a save out of Kenny Arthur but it was easy for the Stanley keeper.
Edwards headed home just after the break but the visitors then upped the pace with the introduction of another striker Jon Nurse.
Shane Huke had a shot cleared off the line while Benson headed over in a good position before Accrington’s Leam Richardson was sent off for a second bookable offence in the 90th minute but the hosts held on for a rare home win.