Star fly-half Johnny Sexton kicked a pressure penalty a minute from full-time to clinch victory after Australia had fought back from eight points down in the second half. Ireland held on to win a three-match series for the first time in the southern hemisphere, to add to their Grand Slam Six Nations victory earlier this year.
Ireland, who trail only world champions New Zealand in the international standings, hadn't won a series in Australia since they swept a two-Test tour in 1979. But Joe Schmidt's team fought back from losing the opening game 18-9 in Brisbane to win the final two Tests in Melbourne and Sydney and end their 39-year away win drought against Australia.
In a gripping second half, the Wallabies clawed back from 17-9 down to close to within one point before Sexton landed his fifth penalty of the night to seal the win. It was a game dripping with controversy as both teams had a player sent to the sin bin and also lost their skippers, Australia's Michael Hooper and Ireland's Peter O'Mahony, to injury in the first half.
The Irish came close to beating another southern hemisphere power, South Africa, in a three-Test series two years ago only to go down 2-1, making this a prized scalp in a brilliant year. But it was a chastening result for Australia, who have lost a home series for the second time in two years after going down 3-0 to England in 2016.
The Wallabies suffered an early blow when skipper Hooper injured his left leg in a clean-out and limped from the field, to be replaced by Pete Samu. Ireland were reduced to 14 men when winger Jacob Stockdale received a yellow card for leading with his elbow to the throat of Wallabies scrum-half Nick Phipps midway through the half.
Bernard Foley kicked the penalty to put Australia in front 6-3. There was controversy in the 31st minute when Israel Folau went for a high ball with O'Mahony, who crashed heavily to the ground.
After intervention from the television match official, Folau was given a yellow card and O'Mahony was taken from the field on a medicab. Conor Murray had a try disallowed by the TMO but in the same incident Adam Coleman was penalised for offside, giving Sexton the easy task of putting Ireland 9-6 ahead near half-time.
Foley and Sexton exchanged penalties, both for offsides, as the Irish turned 12-9 ahead. Ireland once again dominated territory, possession and the run metres in the opening half and at one stage ran through 17 phases in the opposition quarter before the Australians got the ball clear.
The Wallabies again paid for ill-discipline, conceding eight penalties in the controlled Irish attacks. Ireland went on the attack straight after the resumption and after a pinpoint kick from Sexton were deep in Australia's territory. The forwards piled in for a pushover try to CJ Stander off a lineout win to open up an eight-point lead after 44 minutes.
But the Wallabies hit back after Foley's stab kick behind the Irish defence was seized by winger Marika Koroibete, who beat Rob Kearney and took Sexton over the line to score.
Foley converted for the Wallabies to close to within one point, 17-16, after 54 minutes. But Sexton had the final word with a pressure kick from wide out after replacement hooker Tolu Latu was penalised in a maul.