The bottom club needed a win to keep the pressure on St Mirren but the 1-1 draw consigns them to relegation after just one season back in the top tier.
Gary Harkins had had the first attempt on goal but his volley never threatened Jamie Langfield but the Aberdeen goalkeeper was left helpless when the home side went ahead.
Jim McAlister's 12-yard strike took a slight deflection on its way past Langfield (20) to give the Dark Blues the advantage.
Harkins ought to have doubled the lead when he met John Baird's cross six yards out but Langfield was alert to the danger and saved with his legs.
Peter Pawlett promptly took matters into his own hands and only a fine double save from Steve Simonsen kept the lead intact.
The busy Baird was again thwarted by Langfield as the home side continued to dictate before Pawlett threatened for the visitors.
Rory Fallon was then ordered off after an off-the-ball clash with Declan Gallagher but if the home support felt that incident was to turn matters in their favour they were to be sadly mistaken.
Lewis Toshney was deemed to have fouled Pawlett in the box and Niall McGinn ignored the ensuing tumult to crash home the resultant penalty (70).
Langfield repelled McAlister's header and Ryan Conroy also went close but the desperate Dundonians, 15 points adrift at one stage, could not conjure the goal that would have kept their hopes alive - for one more week at least.