West Ham loanee Paul McCallum scored the only goal of the game early in the second half, with the hosts down to 10 men soon after following Joe Rafferty's second booking of the afternoon.
The opening 45 minutes saw little goalmouth incident, Dale enjoying more possession but struggling to create goalscoring opportunities.
Bobby Grant struck the crossbar with an early free-kick and Andrew Tutte forced a save out of Neil Sullivan with a low drive midway through the opening half.
The visitors were more ambitious after the break and Toby Ajala saw a goalbound volley deflected wide before a great double save by Josh Lillis denied Jack Midson and then McCallum in quick succession.
But McCallum was not to be denied in the 56th minute when he side-footed home from six yards after Midson had headed the ball back into the mix when Dale could only partially clear a corner.
McCallum had the ball in the net again soon after but was ruled offside, and the Dons held on comfortably after Rafferty's dismissal for a second late challenge.
