The Wallabies - coached by former Ireland boss Joe Schmidt - stayed in touch at half-time thanks to Len Ikitau and Fraser McReight tries.
But after Sam Prendergast stretched Ireland's lead with a drop-goal and Tommy O'Brien had a try ruled out for a knock-on, Caelan Doris' 70th-minute try ensured a comfortable Irish victory.
Despite losing Nick Frost to a yellow card for his hit on Thomas Clarkson during the Doris score, Billy Pollard went over for Australia's third try.
However, the hosts surged to the finish line as late Ryan Baird and Robbie Henshaw scores capped a much-improved Ireland performance and a fifth successive win over Australia.
With their confidence boosted, Ireland face double world champions South Africa in Dublin on Sunday at 5.40am while Australia end their northern hemisphere tour in France on Sunday at 8.10am.
