"I know it's only the first session but this is how you set the tone for the whole summer," former skipper Michael Clarke said in the Nine Network commentary box.
It could have been even worse for the tourists, who offered half-chances at 2-17 and 3-20.
Hazlewood was the pick of Australia's bowlers, having claimed the prized scalp of Amla with an excellent delivery that nipped off the deck, found the edge and carried to Steve Smith at second slip.
Mitchell Starc struck with the fourth ball of the day, with Mitch Marsh snaffling a remarkable catch at gully to remove Cook.
Duminy unsuccessfully reviewed his caught-behind decision. Third umpire Richard Kettleborough took a long time before deciding there wasn't enough evidence to overturn Nigel Llong's verdict.
The ball appeared to scrape both thigh pad and bat but Duminy immediately referred the decision.
Du Plessis, who boasts a great record against Australia including his defiant ton on debut at Adelaide Oval in 2012, steadied in an unbeaten 46-run stand with Bavuma.
Smith admitted at the toss he was also keen to bat first.