Fourth-placed United missed the chance to open up a seven-point advantage on their opponents - and to leapfrog Hearts - as they were forced to come from behind following Lee Miller's 34th-minute opener.
Craig Levein's side took only four minutes to equalise as David Goodwillie netted for the second time in two matches with a header.
Both sides then had chances to seal all three points, with home substitute Craig Conway striking the post with a free-kick.
However, former United midfielder Mark Kerr ensured the Dons had to hang on for a vital point when he was shown a straight red card for dissent with 14 minutes remaining.
Despite manager Craig Levein's protestations to the contrary, United came into this 'New Firm' derby knowing victory would all-but secure their Europa League spot at the expense of their opponents.
A seven-point advantage with only nine to play for would have presented a formidable task for the Dons but a point apiece means it is still all to play for.
Levein brought back Paul Dixon after suspension and also handed a starting berth to Saturday's match-winner in the 2-1 win over Hibernian, Goodwillie.
Aberdeen were dealt a blow when defender Andrew Considine and Jamie Smith failed fitness tests but manager Jimmy Calderwood was able to bring back Miller following a two-match ban.
The Dons failed to heed the warning posed by United's last-gasp weekend win, with Goodwillie given too much space in the first minute, only to shoot wide.
In the 16th minute Prince Buaben was fortunate to get the break of the ball 30 yards out but he almost made the most of the opportunity as he rifled a drive just over from the edge of the area.
Seven minutes later, the Tannadice side came even closer following a flowing move started by impressive left-back Paul Dixon - but Goodwillie's chip landed on the top of the net.
There was a moment of controversy at the other end in the 25th minute when Darren Dods went down in an off-the-ball clash with Lee Miller, who escaped with only a yellow card.
Having been on the back foot for half an hour, Aberdeen produced a flourish around the home box and netted the opener in the 34th minute.
Lukasz Zaluska comfortably held a volley from Chris Maguire but the Celtic-bound goalkeeper could do nothing when former United striker Miller made the breakthrough with his 11th goal of the season.
Charlie Mulgrew's long corner was headed back across goal by skipper Scott Severin and Miller produced an acrobatic overhead kick from six yards out.
However, four minutes later the hosts were level. Buaben's long ball was magnificently fired into the path of David Robertson and his cross from the right flank was headed powerfully home by Goodwillie.
Aberdeen were forced into a reshuffle at the interval as Lee Mair made way for full-back Javan Vidal, with Ricky Foster moving into a central defensive pairing with Severin.
Sone Aluko almost caught out Zaluska with a cross-cum-shot in the 53rd minute that the Pole tipped over from under his crossbar.
Aluko swerved a shot wide, then cut in from the right flank between Morgaro Gomis and Dixon and producing a low shot which Zaluska touched past the post.
Kerr's deflected drive whistled over and Severin hit the side-netting, before United replaced Danny Swanson with winger Conway.
The visitors were on top and they were almost gifted the lead in the 63rd minute when Mulgrew's free-kick was headed just wide of his own goal by United skipper Dods.
Mulgrew's set-pieces were creating havoc in the United box, with Zaluska looking nervous as he punched another free-kick clear from a crowded six-yard box.
However, just as the Dons looked to be taking a stranglehold on the game, they were reduced to 10 men with 14 minutes remaining.
Kerr was guilty of a high challenge on Conway but, when no punishment seemed to be coming, was then given a straight red card for what appeared to be a volley of abuse at referee Chris Boyle.
Conway struck the post with the resultant free-kick but, with Peter Pawlett on for striker Chris Maguire, and goalkeeper Jamie Langfield touching Goodwillie's shot round his near post Aberdeen succeeded in hanging on for the point in the closing stages.