Brantwood of the Second Division had taken a 15th-minute thanks to Andy Nelson's superb chip over keeper James Taylor from 30 yards.
Dundela equalised early in the second half when Mattie Burrows squeezed the ball in from a tight angle.
David Murphy put the Duns ahead and Burrows struck again to make it 3-1.
The east Belfast side will meet the winners of Wednesday's semi-final between Ballyclare Comrades and Bangor in the Christmas showpiece.