The home team's comfortable winning margin means it has now one hand on retaining the Cormac McAnnellen Perpetual Trophy, with the Australians needing to win by at least 23 points in the Second Test at Croke Park next Saturday to win the series.
The Irish team looked set for a comfortable win when it led by 25 points at the 13-minute mark of the third term.
But the Australians, who had kicked just three overs to that point, fought back kicking a goal and the next three overs to get within eight points at the six-minute mark of the final quarter.
They could have been even closer too with Steven Motlop hitting the top of the crossbar to miss what seemed a certain goal at the five-minute mark of the final term.
But when Ciaran Sheehan scored an over at the 12-minute mark and Kevin McLoughlin scored Ireland's second goal two minutes later the home team had put the result beyond doubt.
Carlton defender Zac Tuohy was the star for the Irish and kicked the first goal of the match halfway through the third term, taking one bounce and kicking the ball to himself twice before slamming it into the left side of the net.
Ireland's win was built on its superiority with the round ball and edge in strength.
Motlop was the standout for the Australians, especially in the first half when they struggled to control the round ball, too often struggling to effectively execute their pre-match strategy of kicking the ball into space.
Lance Franklin had a quiet first term before working his way into the game. He kicked the Australians' second over halfway through the second term and was an important player at the centre ruck contests.
Australian goalkeeper Ash McGrath made a good fist of one of the most difficult roles in International Rules, memorably smothering Sean Cavanagh when he looked set to slot a point-back goal at the five-minute mark of the second term.
Skipper Daniel Wells was also influential through the middle for the visitors, along with Mathew Stokes, while Eddie Betts was lively up forward and Chris Yarran creative in defence.
For the home team, skipper Michael Murphy and Ross Munnelly starred early, each kicking two first-term overs.
Murphy, who was due to play for his local team Glenswilly less than a day after Saturday night's game, was rested for the first half of the third term after the Irish had led by 19 points at half-time.
The Irish set up their win when they kicked five consecutive overs in little more than a quarter from the seven-minute mark of the first term.
The Australians' fightback began late in the third term when substitute Jake Neade accepted a Betts handball and dribbled the ball past the Irish goalkeeper.
Overs to Lewis Jetta and Alwyn Davey and a point to Franklin just before three-quarter time suddenly had the Australians back within 12 points and a chance to pull off a remarkable comeback victory.
It was not to be.
IRELAND 0.5.2 0.8.4 1.9.6 2.12.9 (57)
AUSTRALIA 0.1.1 0.2.3 1.5.6 1.7.8 (35)
GOALS
Ireland: Tuohy, McLoughlin
Australia: Neade
OVERS:
Ireland: Murphy 2, Munnelly 2, Begley, O'Shea, Byrne, Cavanagh, Flynn, Sheehan, Boyle, McManus
Australia: Motlop 2, Franklin, Lew. Jetta, Al. Davey, Stokes, Ler. Jetta
BEST
Ireland: Tuohy, McCaffrey, Murphy, Hanley, McManus, Munnelly
Australia: Motlop, McGrath, Wells, Stokes, Franklin, Betts, Yarran
INJURIES
Ireland: Walsh (leg)
Australia: Nil
Reports: Nil
Umpires: Maurice Deegan (GAA), Matt Stevic (AFL)
Official crowd: 17,657 at Breffni Park
