Newbridge began extra-time with the elements in their favour and Oisin Doherty fired over an early two-pointer, but Beggan hit back from a long free.
It remained level at the change of ends and after Jack McCarron put the Monaghan men in front midway through the second period, McAteer was again to the rescue for Newbridge as he fisted over in added time to leave it 2-20 apiece and send the game into a penalty shootout.
Both sides converted their first two kicks, but Conor Doherty missed the target for Newbridge with Kieran Hughes giving Scotstown the advantage.
After Beggan saved from Sean Young, Darren Hughes stepped up to stroke home and send the Monaghan men into the final against Kilcoo.
Scotstown: R Beggan (0-4, 1x2p, 1x2pf); D McArdle, R O’Toole, D Murray; K Hughes, D Hughes (0-2), D Connolly; M McCarville (1-3, 1x2p), G McPhillips; Max Maguire, S Carey (0-1), F Maguire (0-3); Mattie Maguire (0-3, 1x2p), J McCarron (0-2, 1f), T Mallen (1-2).
Subs: N Sherlock for Max Maguire (51), C McCarthy for F Maguire (53); Max Maguire for T Mallen (ET 5), J Hamill for D Connolly (ET 11), J Carey for Mattie Maguire (ET 16).
Newbridge: N Rocks; C McBride, S McGrogan, M McGrogan; Callum McGrogan (0-1), Conor McGrogan, P McGrogan; C Doherty (1-0), Conleth McGrogan (0-2, 1x2p); E Young (0-2, 1f), M Doherty, C McAteer (0-4, 1x2p); P McMullan (1-0), S Young (0-4, 1x2p), O Doherty (0-6, 2x2p).
Subs: O McGlone (0-1) for P McMullan (45), D McColgan for C McBride (47), K Burke for M Doherty (53); M Doherty for E Young (ET 18), S McAteer for Callum McGrogan (ET 19)
Referee: J McQuillan (Cavan)