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Winger Nick Cummins and flanker Michael Hooper scored early touchdowns as the Wallabies stormed in to a 15-3 lead.
Jonny Sexton pegged it back to 15-12 with three penalties but then had to go off with a hamstring injury.
Australian fly-half Quade Cooper scored the third try in the 46th minute before Hooper got his second of the night.
(provided by Opta)
But the visitors ended the evening with 14 men after centre Tevita Kuridrani received a straight red card for a dangerous tackle on Peter O'Mahony with eight minutes left.
This was just Schmidt's second match since taking over from Declan Kidney, after a comfortable 40-9 victory over Samoa in their first autumn international, but the former Leinster coach will have plenty to ponder before the meeting with his native New Zealand in Dublin on 24 November.
Ireland's narrow defence allowed Australia to grab early control and, although the deficit was reduced to three points for a while, Australia claimed a comprehensive victory while denying their hosts a single try.
Just 24 hours earlier, the same stadium had witnessed what Irish football fans will hope is a new dawn as new managerial pairing Martin O'Neill and Roy Keane kicked off their reign with a 3-0 win over Latvia.
And there had been a similar feelgood factor in rugby circles following the appointment of the astute Schmidt - but long before the final whistle sounded there were thousands of stunned supporters silently trudging homeward after a definite reality check.
Cooper opened the scoring with a ninth-minute penalty after Ireland's offside offence, though Ireland responded with Sexton levelling from the tee on 12 minutes.
Cooper then missed what looked a straightforward penalty, but Australia were soon back in front through their first try, from Cummins in the 17th minute.
The left wing cut in to expose weakness in the home defence after a midfield break from hooker Stephen Moore.
The Irish line was breached again on 24 minutes as Hooper accepted Scott Fardy's back-handed offload for an easy run-in.
Cooper's miss from the conversion was little comfort to a clearly stunned Irish side.
Schmidt's charges did whittle away at the deficit through Sexton's penalties, and open-side Hooper was sin-binned for not rolling away, but the reality was that Ireland had rarely threatened the Australian line.
Cooper crossed for a try six minutes after the restart as confusion between Luke Marshall and replacement fly-half Ian Madigan presented the the Aussie number 10 with a gap.
And another Cooper penalty extended the visitors' lead to 25-15, Madigan claiming three back with a penalty.
Hooper scored his second try as Australian barged over after a line-out, with Cooper's conversion making it 32-15.
Even when they thought they had grabbed a late consolation try, Ireland were to be confounded - penalised for a knock-on in the build-up as replacement Sean Cronin touched down.
Ireland: R. Kearney, Bowe, O'Driscoll, Marshall, McFadden, Sexton, Reddan, Healy, Best, Ross, Toner, O'Connell, O'Mahony, O'Brien, Heaslip.
Replacements: Henshaw for R. Kearney (73), Madigan for Sexton (41), Murray for Reddan (56), Cronin for Best (65), Archer for Ross (65), McCarthy for Toner (70), McLaughlin for O'Brien (73).
Not used: McGrath.
Australia: Folau, Ashley-Cooper, Kuridrani, Toomua, Cummins, Cooper, Genia, Slipper, Moore, Kepu, Simmons, Horwill, Fardy, Hooper, Mowen.
Replacements: Tomane for Ashley-Cooper (57), Lealiifano for Cooper (70), White for Genia (65), Ryan for Kepu (65), Timani for Horwill (56).
Not used: Polota-Nau, Robinson, Gill.
Sin bin: Hooper (32).
Sent off: Kuridrani (73).
Att: 46,000
Referee: Chris Pollock (New Zealand)
Touch judges: Romain Poite (France), Stuart Berry (South Africa)
TV: Geoff Warren (England)
Ireland coach Joe Schmidt suffered a heavy first defeat in charge as Australia ran in four tries at the Aviva Stadium on Saturday.