With this deciding game, the Hoops showed why they won the league with a determined and valiant effort against a United side who did not lie down.
Jan Vennegoor of Hesselink scored the decisive goal in the 72nd minute which had the visiting bench dancing with joy and applauding their team's ability to break down a resolute United defence.
The Terrors had their fair share of chances and pressed the Hoops at every opportunity.
Their best chance in the first half came in the 21st minute with a wonderful break from Willo Flood ending with a deep cross which Danny Swanson scooped over from only four yards.
This was closely followed by Mark De Vries' shot from 12 yards which narrowly missed after magnificent work again by Flood.
In an evenly matched first half, Lukasz Zaluska brilliantly tipped over an Aiden McGeady volley as Shunsuke Nakamura broke with pace.
The keeper again showed that he was giving no favours to his Polish friend, Artur Boruc, when he brilliantly tipped over Barry Robson's header which was going into the top corner.
With the crowd in full voice, Nakamura almost opened the scoring in the 48th minute, but his low shot was blocked by the lunging legs of Darren Dods.
The Japanese midfielder followed up with a theatrical dive which earned him a yellow card.
The game continued to swing like a pendulum with Boruc having two fantastic saves on the hour mark.
Firstly, he tipped De Vries' left-foot shot just over, then he repeated the brilliance with Swanson's half-volley.
The news filtered through from Pittodrie that Rangers were one down and this seemed to lift the Celts with Vennegoor of Hesselink claiming that all important winner.
The goal itself paled into insignificance as the news came through of Aberdeen's second and the league flag headed back to Parkhead for the third consecutive year.