The Hoops went into the match needing just one point to wrestle control of the Scottish Premiership back off rivals Rangers and managed exactly that at Tannadice Park.
Celtic looked set to get over the line in victorious fashion when Giorgos Giakoumakis opened the scoring with his 15th goal of the campaign, but Dylan Levitt hit back for the hosts.
In the end, it was a result that suited both teams as Ange Postecoglou was able to savour confirmation of title glory in his first season in charge of the Parkhead side, while United sealed their place in the Europa Conference League qualifiers.
Home manager Tam Courts made six changes to the team that lost 2-0 to Rangers on Sunday as he opted to rest some key men ahead of what could potentially have been a European shootout with Ross County this Saturday.
Celtic had the first opportunity of the night after three minutes but Anthony Ralston fired an angled shot over the bar from 10 yards out after being set up by Matt O'Riley following a quickly-taken corner by Forrest.
The Hoops threatened again five minutes later as Forrest saw a powerful shot from inside the box deflected over by Liam Smith.
Reo Hatate shot over from the edge of the box in the 19th minute and the Japanese midfielder went close again on the half hour when he pinged a powerful angled strike just over from 15 yards out after playing a one-two with Giakoumakis.
United's first attempt of the match came four minutes before the break when Archie Meekison shot over from the edge of the box.
Celtic made the breakthrough in the 52nd minute when Giakoumakis powered home a close-range header after being picked out by an excellent Ralston cross from the right.
United thought they had equalised five minutes later when Nicky Clark followed up to force the ball home after teenager Rory MacLeod had hit the inside of the post from 20 yards out but the linesman's flag cut short the hosts' celebrations.
The hosts went close again in the 62nd minute when substitute Tony Watt headed against the post and Ilmari Niskanen bundled the rebound wide of the target.
Celtic almost doubled their lead five minutes later but United goalkeeper Benjamin Siegrist got down to make a sensational save to stop Jota's powerful strike from inside the box nestling in the bottom corner. Giakoumakis then shot just wide from 10 yards out as the visitors looked to kill the game.
But United went straight up the park and levelled in the 72nd minute when Levitt fired a stunning strike past Joe Hart from the edge of the box.