Neil Lennon's side had clinched their third successive title with a 5-1 win over Partick Thistle on Wednesday night and were looking to put on a show for their supporters, but the home crowd was silenced in the 15th minute when Dutch striker Melvin de Leeuw fired the visitors ahead.
Kris Commons equalised from close range in the 34th minute and both sides hit the woodwork after the break before settling for a point which better suited the visitors, who are battling to remain out of the relegation play-off spot.
Niall McGinn scored his first goal in 17 games to earn Aberdeen a point against Dundee United in the race for second place.
The Northern Ireland winger struck seven minutes after the interval to cancel out an early strike from his international colleague Paul Paton as the match finished 1-1.
A cracking Craig Slater goal five minutes into injury-time gave Kilmarnock a precious 2-1 victory over Motherwell to steer them further away from the relegation play-off spot.
A first-half goal from Iain Vigurs should have set the home side up for a win to enhance their chase for a Europa League spot, but Rory McKenzie's second-half equaliser brought Killie level and set up a grandstand finish.
Inverness and St Mirren missed out on the opportunity to close the gap on the teams above them with a 2-2 draw at Tulloch Caledonian Stadium.
The visitors took a third-minute lead through Jason Naismith, but goals by Ross Draper in the 16th minute and Greg Tansey 19 minutes later turned the match in the favour of Inverness before the interval.
Sean Kelly brought St Mirren level just past the hour mark and the Buddies looked to have been handed the initiative when Josh Meekings saw red with 23 minutes still remaining, but the hosts held on.
Kris Doolan's 90th-minute strike rescued a deserved point for Partick in a 1-1 draw with St Johnstone.
The second-half substitute struck with time running out after the Jags had dominated for most of the match but trailed to Stevie May's early opener.