Replacement fly-half Byrne nailed a difficult kick from wide on the right with just three minutes remaining in Dublin to earn Ireland a record-equalling 12th successive home victory.
Andy Farrell’s men struggled for large parts of a disappointing contest and could easily have ended 2022 with a serious reality check against opponents beaten by Italy just last weekend.
A difficult evening for the Irish began with talisman Sexton withdrawing through injury, with his deputy Jack Crowley booting five points on his maiden Test start before Byrne, who was elevated to the bench at the 11th hour, proving to be the match-winner.
Victory for Ireland saw them become the first nation to defeat New Zealand, South Africa and the Wallabies in a calendar year since England in 2002.
Sir Clive Woodward’s men went on to lift the World Cup the year after achieving that feat and that remains the ultimate goal for Farrell’s side looking ahead to next year’s showpiece tournament in France.
On this evidence, that dream seems a distant reality.
Farrell was far from pleased with what he witnessed in last weekend’s underwhelming 35-17 win over Fiji and – Sexton aside – welcomed back a host of players from injury as part of eight alterations.
The world coach of the year nominee would have taken little encouragement from a painfully stop-start encounter littered with sloppy errors, penalties and exchanges of possession.
Ireland defended doggedly in the face of incessant pressure for large parts of the opening period, including at one stage repelling 21 phases which sparked a rousing rendition of the Fields of Athenry, but offered little from an attacking perspective.
Australia thought they had scored a fourth-minute try, only for scrum-half Nic White’s effort to be disallowed on review due to Dave Porecki’s neck roll on Josh Van Der Flier.
Crowley, wearing the number 10 jersey embroidered with Sexton’s name, calmly slotted the only points of the half in the 10th minute, while rival fly-half Bernard Foley was wayward with a penalty at the other end.
Wallabies coach Dave Rennie had retained just five of the players who began the embarrassing 28-27 loss in Florence.
Replacement hooker Folau Fainga’a was among the 10 men dropped and, having come on to replace the stricken Porecki, was sin-binned in the 37th minute after Van Der Flier endured another high tackle, before Irish number two Dan Sheehan was held up on the line just before the whistle.
A poor – and, at times, tetchy – Test match was in desperate need of a spark.
Ireland scrum-half Jamison Gibson-Park looked to have provided it seven minutes after the restart but his score was subsequently chalked off as Canberra-born team-mate Mack Hansen had gone into touch just before a fine offload.
Australia had briefly been reduced to 13 men at that point due to the temporary absence of Fainga’a prompting uncontested scrums.
The Wallabies came through a crucial period in the contest unscathed and were level in the 56th thanks to Foley finding his range with his second penalty.
Below-par Ireland eventually made a significant dent on the scoreboard 10 minutes later when replacement Aki came back with a bang by bulldozing over at the end of relentless pressure which prompted the sell-out crowd to finally find their voices.
Crowley added the extras but the joy was swiftly cut short as Wallabies substitute Petaia broke clear to cross wide on the right, with Foley landing the tricky conversion.
Ireland looked like they would have to settle for a rare draw but Byrne impressively held his nerve as the world’s top-ranked team scraped a ninth win from 11 Tests to round off an unforgettable year in unconvincing but victorious fashion.