Galway’s Gary Kelly gave his side the edge with a free in the first period of extra-time, but three points in a row for Roscommon — two from Murtagh either side of Kieran Kilcline’s point — sealed the win.
But for long periods at Tuam Stadium on Saturday evening it looked as the champions would bow out. Eoin McCormack looked to have given Galway the win with his goal seven minutes from time, but two late frees from Thomas Corcoran pushed the game into extra-time.
After Roscommon raced into an early 0-2 to 0-0 lead with points from Michael Gunning and Murtagh, Galway dominated as Kelly and Jason Lyons hit two points each to give the Tribesmen the lead.
However, an excellent goal in first-half injury-time from Ronan Daly gave Roscommon a 1-3 to 0-4 advantage at the break, but they were made to work all the way for the win.
After McCormack goal Liam Silke pushed Galway into a two-point lead and they looked set for the win, but Corcoran’s late frees in normal time kept the Rossies in the tie and Murtagh completed the victory in the 82nd minute.
Roscommon now face Mayo in the Connacht final at Hyde Park on Sunday week.
Scorers for Roscommon: D Murtagh 0-6 (3fs), R Daly 1-0, T Corcoran 0-3fs, M Gunning, K Kilcline 0-1 each.
Scorers for Galway: G Kelly 0-5 (4fs), E McCormack 1-0, J Lyons 0-2, J Heaney, L Silke 0-1 each.
ROSCOMMON: S Mannion; P Neilan, D Barron, C Kenny; T McKenna, C Hussey, R Daly; U Harney, T Corcoran; C Compton, R McManus, E Smith; D Murtagh, K Finn, M Gunning.
Subs: B Fannon for McManus (35), N McInerney for McKenna (36), K Kilcline for Compton (50), C Casserley for Gunning (60), C Compton for Casserley (70).
GALWAY: R Lavelle; A Nolan, J Kennedy, E Wynne; L Silke, C Cunningham, E Kerin; S Lawless, M Daly; J Lyons, B McHugh, A Meeneghan; E McCormack, G Kelly, S Hughes.
Subs: J Heaney for Meneghan (20), G Gibbons for Kerin (37), M Upton for Lawless (39), A Menehan for Hughes (58), E Walsh for Cunningham (77), C Slattery for McHugh (78).
Referee: F Flynn (Leitrim).