The match looked to be coasting towards a draw before Liam McAlinden headed in from an 81st-minute free-kick after Dons substitute Sanmi Odelusi received his second yellow card in two minutes.
That sent the 8,943 travelling fans - who helped set a new stadium mark of 20,516 - into raptures and was enough to secure the three points.
The victory moved Wolves six points clear at the top of League One and Jackett admitted he could not have asked for more.
"You couldn't write the script, really. Ten minutes to go and the substitute comes on and heads in the winner right in front of our fans," he said.
"It's not every day that you can celebrate a 1-0 win in front of 9,000 away fans, so it's been a fantastic day for us and for me as a head coach. It was great for our season.
"I thought the pitch spoiled the game. You've got two very good football teams and MK Dons were just as keen as us to get the ball down the park, but it wasn't possible.
"It was like playing a football match on a rugby pitch. It took the quality away.
"At this stage of the season, results are everything. We had to make sure that we just kept defending and didn't get frustrated going forward.
"We found a way to win, and it was a great win. When the chance did come, we took it."
Odelusi was booked twice in the space of two minutes for repeat fouls on Scott Golbourne, having only appeared as a substitute just before the hour.