With 92 minutes on the clock, Boulding found the bottom left-hand corner of the net from inside the box after latching onto Keith Watson's assist.
The result means Craig Brown ended his 28-month spell as Dons' boss with a disappointing defeat in a match that yielded very few chances.
Brown now moves up stairs at Pittodrie to be replaced by Derek McInnes who will take charge of the club for the remaining five games of the season.
Aberdeen had also kicked off with a chance of finishing above the SPL cut line and, for most of the contest, they edged a poor game in terms of chances.
In a dull first half, Niall McGinn fizzed a free-kick inches wide of a post while, at the other end, Ryan Gauld missed a good chance for the hosts.
Jon Daly ballooned an effort over while home keeper Radoslaw Cierzniak did well at the start of the second half to push away a McGinn header.
The woodwork saved the Dons when a Willo Flood header rebounded off the cross bar before visiting keeper Jamie Langfield denied Daly.
Langfield came to the rescue again moments later with a brilliant double save, first blocking Gauld and then blocking Daly.
McGinn tested Cierzniak who also pushed away Rory Fallon's long-range effort as the visitors chased three points.
But with both sides seemingly heading for a point, up stepped second half substitute Boulding to score his first goal since moving to Tannadice on loan and sneak United into the top six.