Defeat for Kilmarnock at the hands of Dundee, combined with the late strike at Tannadice, ensured United a place in the top half of the Clydesdale Bank Premier League table beyond the split.
Killie had been in the driving seat to claim the top six berth, with United, the Dons and Hibernian also in contention at the start of the day.
The visitors threatened from a couple of set-pieces in the first half. First Niall McGinn's free-kick from just outside the box fizzed past the upright then Russell Anderson glanced a header wide from Jonny Hayes' delivery.
At the other end, Jon Daly then squandered a great chance to grab the opener just before the interval, ballooning over when he should at least have tested Jamie Langfield.
The Dons were out of the traps quickly after the break and Radoslaw Cierzniak was called into action to beat away McGinn's header a minute after the restart.
Gary Mackay-Steven was brought into the action after 53 minutes and the winger immediately lit up the match for the home side. He burst through on goal and looked certain to find the back of the net but delayed pulling the trigger and allowed Mark Reynolds to make a superb block before he could unleash the shot.
The woodwork then prevented United from opening the scoring when Langfield blocked a Ryan Gauld shot and Willo Flood's follow-up header smacked off the crossbar, before Mackay-Steven eventually nodded over.
United pushed forward in numbers and the Aberdeen goalkeeper did well to claw a net-bound Daly header away from the gaping net, before coming to the rescue again moments later with a brilliant double save, firstly blocking Gauld's header and then preventing Daly's shot from finding the target.
The match ended in dramatic scenes when Boulding kept his composure to rifle past Langfield deep into injury time to secure the last top-six spot.
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