Ireland now take a 57-35 lead into the second leg at Croke Park next weekend.
And captain Murphy led by an example, scoring two early score as the hosts ended the opening quarter 17-4 ahead.
Ireland led 28-9 at the halfway stage, and Zac Tuohy’s strike was cancelled out by a Jake Neade goal as Australia clawed their way back and finally showed some of the determination which made them favourites.
Kevin McLoughlin scored a goal towards the end to give Ireland a deserved cushion ahead of Croker.
Neil McGee and Paddy McBrearty also put in tough performances in the game.
For Murphy, he’s in the car on his way home – ready for battle for Glenswilly against Killybegs in the county final tomorrow.
Ireland: P O’Rourke, C McKaigue, P Hanley, N McGee, L Keegan, Z Tuohy (1-0-0), J McCaffrey (0-0-1), A Walsh, S Cavanagh (0-1-0), P Flynn (0-1-1), C Byrne (0-1-1), C Sheehan (0-1-0), P McBrearty, M Murphy (0-2-1), R Munnelly (0-2-2).
Interchange players: C Begley (0-1-0), A O’Shea (0-1-0), C Boyle (0-1-0), K McLoughlin (1-0-0), C McManus (0-1-1), C Kilkenny (0-0-1), M Shields, P Conroy.
Australia: A McGrath, C Yarran, T Armstrong, C Ellis-Yolmen, J Harbrow,, N Lovett-Murray, Lewis Jetta (0-1-0), D Wells (0-0-1), L Franklin (0-1-4), M Stokes (0-1-0), J Hill, Alwyn Davey (0-1-0), S Motlop (0-2-2), L Thomas, E Betts.
Interchange players: S Edwards, S Wellingham, Leroy Jetta (0-1-0), J Neade (1-0-0), D Barry, Aaron Davey (0-0-1).
Referees: Maurice Deegan (Ire) & Matt Stevic (Aus)