Aki try on return helps Ireland edge Australia to equal home record
A late penalty by Ross Byrne separated the two sides in a dramatic climax to a match littered with errors.
The Irish will enter the World Cup year ranked number one in the world and are the first team since England in 2002 to defeat the All Blacks, the Springboks and the Wallabies in a calendar year.
England went on to win the World Cup in 2003 but based on this performance the Irish will need to up their game significantly even to make the semi-finals for the first time.
"I'm absolutely delighted with the win," said Ireland head coach Andy Farrell.
"We found a way and that's what good sides do when they're not at their best.
"We weren't at our best for all sorts of reasons, things that we can address.
"We found a bit of luck but we came out on the right side and we roll onto the Six Nations."
For Australia it was a third successive narrow defeat in the Autumn Nations Series - having lost by a point both to France and then in an historic defeat to Italy.
"100% put pride back in the jersey after the Italy defeat," impressive Australian wing Mark Nawaqanitawase told Amazon.
"We're definitely gutted. We got ourselves in the right position there.
"Discipline has been one of the things we're working on and obviously it's hurt us again - as a result, we've come so close."
Sexton had been ruled out shortly before the teams came out having injured his calf muscle in the warm-up.
Sexton's replacement at fly-half Jack Crowley passed his first test by converting a penalty to give the hosts the lead after a nervy opening.
Veteran Australian fly-half Bernard Foley missed a great chance to level the match in the 21st minute but his penalty went wide of the posts.
The Australians looked the most dangerous of the two sides when they had possession and Nawaqanitawase took the eye in particular.
Jordan Petaia also made a defence splitting run but was brought to ground and in the process lost a boot - he valiantly tried to continue as the Wallabies kept possession but was slipping and sliding all over the place.
Superb Irish defence, though, kept the Australians at bay and finally after 26 phases of play Caelan Doris forced a turnover allowing them to clear.
'A positive note'
However, the Irish then let the Australians off the hook by conceding a penalty inside the visitors 22 - referee Ben O'Keeffe telling both captains that another tackle round the neck would result in a yellow card.
O'Keeffe's warning fell on deaf ears with Folau Fainga'a who got Josh van der Flier round the neck and was shown the yellow card without too much standing on ceremony four minutes from the break.
The second-half took a while to warm up and Foley levelled the match 15 minutes in with a sweetly-struck penalty.
The Irish finally put an incisive attack together - spear-headed by Doris - Aki rounding it off.
Crowley converted for 10-3 with just over 12 minutes remaining.
The visitors, though, hit back as Petaia went on his own despite an overlap and touched down - Foley converted for 10-10 with 10 minutes remaining.
The Irish, though, retook the lead when Ross Byrne, who had come on for Crowley, kept his nerve and landed a penalty with less than four minutes to play.
There looked set to be a late twist as the Australians pressed deep in Irish territory but twice they surrendered possession and it was with some relief that the Irish greeted the final whistle.
Australia's coach Dave Rennie bemoaned the fact his side conceded so many penalties (12) with defeat putting even more pressure on him with just four wins in 16 Tests since the beginning of November 2021.
"It's frustrating because a number of those happened when we were in attacking positions," Rennie told Amazon.
"We'll put out a good side next week (against Wales) and look to finish on a positive note."
