Paceman Josh Hazlewood led the Australian attack in the absence of injured Mitchell Starc, taking six for 70 off 24.5 overs.
Victory would give Australia a 2-0 win in the three-match series with the Kiwis bidding to remain unbeaten in their last eight Test series since 2013 if they can bowl out the Australians with the pink ball.
Whichever way it goes, the Adelaide Oval is poised for its first three-day Test match in 64 years since the West Indies beat Australia by six wickets.
B J Watling fell on the ninth ball of the day on his overnight score of seven.
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Hazlewood got an edge which flew to second slip and skipper Steve Smith, who dropped him on two the previous evening off the same bowler.
Hazlewood claimed his fifth wicket of the innings with the caught behind dismissal of Mark Craig for 15.
Santner's impressive knock came to an end on a rush of blood after jumping down the wicket to crash spinner Nathan Lyon for six.
Tim Southee then hit two fours and went after Mitch Marsh to be well caught by Lyon on the backward square boundary rope for 16.
Trent Boult went for a wild swing and was bowled by Hazlewood for five to end the innings with Doug Bracewell remaining unbeaten on 27.