Chris Cohen headed in Ben Osborn's cross to put Forest ahead early on but Nicky Maynard levelled with a close-range finish from Josh Murphy's cross.
Reds defender Danny Fox was shown a straight red card shortly before half-time for fouling Jordan Spence.
But Osborn's skill set up Assombalonga to net his first goal for 15 months since returning from long-term injury.
Maynard missed a golden chance to put the hosts ahead after the break, firing over from four yards, while Ryan Mendes grazed the crossbar for the visitors.
Forest, whose 17-month transfer embargo is set to end, finished the season 16th after their second win for caretaker manager Paul Williams in what was expected to be his final game in charge.
The Dons ended their first season in the Championship in 23rd place after picking up just four points in a miserable 11-match winless run.
MK Dons manager Karl Robinson: "We performed OK and we've probably scored the goal of our season.
"In the second half it did look like two teams who had nothing to play for, it was hard at times sitting here with the lack of intensity through both sides.
"Now the season is over it's about us rebuilding, the line is drawn now and we just need to forget about the disappointments of this season."
Nottingham Forest interim manager Paul Williams: "It was kind of mind-blowing how many of our fans were here. We had nothing to play for and it just shows you the size of Nottingham Forest.
"Chris Cohen has not scored for a long time and he pops up and scores and then it's really written in the stars that Britt has come on and scored the winner.
"You could see what it meant to the staff, the players and the fans with the way he celebrated."
Substitute Britt Assombalonga's winner gave 10-man Nottingham Forest the points at already-relegated MK Dons.