The seemingly unlikely comeback at the end of regulation came after a dramatic second-half that had begun with Scotstown leading 0-6 to 0-1.
Kilcoo were playing into the considerable wind in the first half with the conditions hampering their attacking efforts.
Despite a sizeable edge in possession through the opening period, there were just five minutes until the break before they registered their sole score of the first half.
The point was provided by Eugene Branagan, but even the wavering trajectory of the ball as it bisected the posts was evidence of the difficulties endured by the Down side’s players when shooting into the swirling breeze.
By that stage, Beggan had already kicked the first pair of two-pointers among his tally and there seemed only one winner when his side’s lead was stretched to eight midway through the second half.
But, having struggled to find their range with the wind at their backs in the early stages of the second half, Kilcoo belatedly mastered the conditions to reel Scotstown in.
Devlin finally got his side off the mark in the second half with a two-pointer 13 minutes after the restart, with the forward adding a further three points as the Down champions cut the deficit to only a point in the closing stages.
A drilled effort from Kieran Hughes was matched by Tommy Mallen from just inside the arc, before Beggan stepped up with another two-pointer to give his side that seemingly crucial three-point cushion heading into injury time.
But his Kilcoo counterpart Niall Kane answered in kind with the clock already well in the red.
Rather than mere consolation, Kilcoo regained possession with the three minutes of indicated added time already up and Callum Rogers gathered and spun brilliantly to send the game into extra time.
Rather than be flattened by letting the long-sought title slip from their grasp, Scotstown lifted themselves from the floor in extra-time with Beggan kicking two frees and a 45, in addition to three points from Conor McCarthy, to end their 36-year wait.