Kris Commons netted with 11 minutes left for the Hoops, who struggled to create chances against the Dons.
Darren McGregor's stoppage time header salvaged a point for St Mirren from an entertaining 2-2 draw with Inverness at St Mirren Park.
Debutant Lewis Guy had given the hosts the lead just after the half hour mark but two goals in the final 20 minutes from Nick Ross and Billy McKay had appeared to have handed the visitors all three points, before McGregor's header meant the home side got a share of the spoils.
Hearts secured a less-than-comfortable 2-0 win over St Johnstone at Tynecastle despite the visitors playing over half of the match against 10 men.
John Sutton's 30th minute penalty and a late David Templeton strike separated the two sides with Saints' striker Gregory Tade shown a red card for a scuffle in the box six minutes before half-time.
Premier League new boys Ross County extended their unbeaten league run into the top flight as a goalless draw with Motherwell made it 35 games without defeat.
County produced a solid top flight debut and restricted Motherwell to very few chances at the revamped Global Energy Stadium in Dingwall.
Fellow Premier League new boys Dundee enjoyed a respectable return as they claimed a point after holding Kilmarnock to a goalless draw.
Their route to the SPL may have been unusual and controversial in the eyes of some, following Rangers' demotion, but Dundee demonstrated an ability to hold their own following a seven-year absence from the top division.
