The world’s number one side were pushed to the limit by the Wallabies, who turned down a chance to draw the game with a late kick to the corner.
As had been the case for much of the game though, they infringed while in possession, and Ireland hung on to clinch the win.
The home side had been dealt a blow before kick-off when skipper Johnny Sexton was ruled out due to a calf injury he picked up in the warm-up.
That meant a start for Jack Crowley, who had only made his debut against Fiji last week and has fewer than 20 appearances to his name for Munster.
The 22-year-old did not look overawed though, kicking a first-half penalty, the only points from either side.
Australia had most of the ball, but struggled to make it count. They finally drew level ten minutes into the second half, Bernard Foley slotting a penalty.
But when Bundee Aki went over with ten minutes to go, it looked as though Ireland had finally done enough.
The lead lasted barely two minutes, Jordan Petaia responding for Australia, but a scrum penalty gave Byrne the chance to snatch it from 45 metres out on the angle, and he made no mistake.
EARLY FLURRIES
The opening minutes were full of drama. The Wallabies thought they had a try when Nic White spotted a gap around the fringes and darted over. His joy was short-lived though, Dave Porecki penalised for a neck roll in the build-up.
To rub salt into the wounds, Hunter Paisami limped off after picking up a knock in the move, replaced by Petaia.
Australian discipline was an issue, and when they failed to roll away from a breakdown, Crowley overcoming the nerves of playing the biggest game of his career to slot the three.
Foley could have levelled matters for the Wallabies when Ireland were caught offside from Jamison Gibson-Park’s box-kick, but he was uncharacteristically off-target.
Both teams were struggling to find their fluency, Australia dominating possession and territory but unable to break down the resilient Ireland defence.
The home side, meanwhile, found themselves on the back foot for much of the half, only able to clear their lines through Australian penalties.
But those kept coming, replacement Folau Fainga’a sent to the sin-bin for the fourth such incident right before half-time.
That gave Ireland their best chance of a try as they turned down a shot at goal to go to the corner. It almost paid off but Dan Sheehan was stopped short of the line by White, before Gibson-Park stepped into touch.
THE 13 MEN HOLD OUT
Trailing 3-0 at half-time, Australia then had to withstand two minutes with 13 men, with both hookers off the field and uncontested scrums.
Despite the two-man advantage, Ireland could not find a way through, Mack Hansen forced into touch just before an offload to put Gibson-Park in.
It was not until ten minutes to go that a try was scored, Caelan Doris with a clever peel off a lineout to get Ireland on the front foot. Australia were scrambling and eventually the ball was shifted wide for Aki to squeeze it down.
Australia’s response was immediate, Will Skelton shaking off six defenders on one monster carry that opened up the space on the right for Petaia to get over. Foley converted and it was all square with nine minutes to go.
There was more drama to come, Ireland winning a scrum penalty that Byrne converted with remarkable poise to put his team ahead.
Australia could have gone for the draw when Ireland were then pinged near their own 22, but they instead went to the corner for the win. It did not work out, their maul penalised for players joining in front of the ball, and despite stealing a final lineout, they did not have a better chance.
