It was a second win for Ireland in the November series after last week’s triumph over Japan, while the Wallabies have now lost three in a row after being beaten by England and Italy.
The 27-year-old Hansen, who moved from Australia, where he played for the ACT Brumbies, to compete for Ireland for whom he qualifies through his Cork-born mother, crossed the line three times in the opening 28 minutes at a rainy Dublin Arena.
Captain Caelen Doris, Ryan Baird and Robbie Henshaw scored Ireland’s other tries while Sam Prendergast kicked a drop goal and two conversions, and his replacement Jack Crowley added a penalty and three conversions.
Australia scored two first-half tries through Len Ikitau and Fraser McReight and a late consolation from Billy Pollard. James O'Connor kicked two conversions.
Ireland burst into a sixth-minute lead as Hansen darted between the posts at the end of a quick tap that caught the Wallabies napping.
The second try, five minutes later, was almost a carbon copy of the first, with Stuart McCloskey bringing Ireland to within a metre out with a hard carry off the scrum, before a wide pass to Robbie Henshaw was pulled back for Prendergast to send Hansen straight through a gap under the posts.
Australia’s first try came in the 17th minute off a lineout maul, with Ikitau powering over, but Hansen, playing at fullback for Ireland for the first time, completed his hat-trick after Prendergast’s crossfield kick found Tommy O'Brien, and although he was tackled, the ball spilt for Hansen to burst over.
"That is the pleasure of playing with this team, I just had to grab the ball and run over the line, I didn't really have to do much," Hansen said.
Australia, however, reduced the score to 19-14 on the stroke of half-time when McReight scored at the end of multiple phases with a pick and go.
The opening 15 minutes of the second half proved attritional and without any more score until Prendergast put over a drop kick to extend the home side’s lead to eight points.
Prendergast’s replacement, Jack Crowley, extended the lead with a penalty from close-in as Ireland dominated territory amid a litany of Wallaby errors.
Doris scored at the end of sustained home pressure as Ireland breached the 30-point mark against Australia for the first time in the 39 Tests between the two countries.
A yellow card to Nick Frost initially made no difference as Pollard scored for Australia, but Ireland made full use of the numerical advantage as Baird and Henshaw scored tries in the last three minutes.
