The visitors were in control thanks to goals from Padraig Amond and Peter Murphy and although Sammy Moore struck in injury time, it wasn't enough for the struggling Dons to get anything from the game.
The home side started the better and Christian Jolley weaved his way into the box before flashing a shot across the face of goal.
But Stanley took the lead against the run of play, Will Hatfield's shot initially stopped by Seb Brown but the ball looped into the path of Amond, who finished with a neat chip for his fifth goal of the season.
After half-time Jolley was wasteful with two chances and was made to pay as the Dons found themselves two goals down with little over 10 minutes remaining, Murphy firing home a stunning volley to register his third goal in his last four games.
Moore tapped home from six yards to give his side some hope but it was too little, too late as Accrington racked up back-to-back league wins.