With Hampden out of commission due to the forthcoming Commonwealth Games, the match took place at Celtic Park.
The teams played out a 0-0 draw in a tense encounter of few chances before Derek McInnes' men won the shoot-out in front of 51,143 fans.
Adam Rooney scored the decisive penalty as the Dons won 4-2 on spot-kicks to claim their first silverware since 1995/96.
Watch: Match highlights on the SPFL YouTube channel
The winning team
Jamie Langfield
Shay Logan
Russell Anderson
Mark Reynolds
Andrew Considine
Barry Robson
Willo Flood
Ryan Jack
Jonny Hayes
Niall McGinn
Adam Rooney
Substitutes
Nicky Weaver
Alan Tate
Nicky Low
Scott Vernon
Cammy Smith
