The Black Caps, needing a win to draw the three-Test series after losing the Brisbane opener, opted to bat after winning the toss in the much-anticipated Test match featuring a pink ball for the first time.
The Kiwis had largely negotiated the opening hurdle with only the loss of opener Martin Guptill before pace spearhead Mitchell Starc trapped Williamson leg before wicket for 22 nearing the first interval.
Starc, who has taken over as the leader of the Australian bowling attack after last week's retirement of Mitchell Johnson, hit Williamson's pads with a yorker in front of the stumps with the fourth delivery of his second over in a new spell.
The Adelaide crowd had grown to more than 30,000 under sunny skies for the much-hyped first day-night match in 138 years of Test cricket.
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The substantial interest in the trailblazing day-night Test was how the new pink ball would react under lights later on the opening day.
Guptill lasted nine balls before he was trapped leg-before for one in Josh Hazlewood's second over.
Guptill was rapped on the back pad and did not seek to challenge the umpire's call after consulting with his batting partner Latham.
New Zealand, unbeaten in their last seven Test series since 2013, will have to win the historic Test to draw the series after Australia won the Brisbane opener by 208 runs and last week's second Test in Perth finished in a high-scoring draw.