Wayne Burnett's side extended their unbeaten league run to five games, recording back-to-back league victories for the first time since December, while James Beattie's Stanley are still hunting for their first Sky Bet League Two win of the season with 10 games gone.
It was an even first half with Hines racing clean through but forcing a great save out of Marcus Bettinelli
Soon afterwards Stanley midfielder Peter Murphy saw his header from a Lee Naylor corner cleared off the line.
Visiting striker Murphy tried a back flick just before half-time which Bettinelli read to keep it goalless at the break.
After the interval, Shay McCartan headed into the side-netting from a few yards out as the hosts looked to break the deadlock.
However, it was Dagenham & Redbridge who took the lead after 56 minutes when Murphy broke through and played in Hines, who fired beyond the outstretched arms of Bettinelli.
And another counter attack five minutes later saw the Daggers double their lead. This time Hines broke clear and set up Murphy who finished with a low shot into the bottom corner of the net.
Stanley pulled a goal back in the first minute of injury time when Will Hatfield's long-range effort was spilled by Chris Lewington and James Gray followed up. But it was too little, too late.