New Zealand managed only one wicket from the first two sessions on Friday, placing Williamson’s decision to send Australia in to bat upon winning the toss under an even harsher light.
Australia's pacemen struck twice to leave New Zealand vulnerable at 44 for two on day two of the Boxing Day test after Travis Head scored a sparkling century to put the hosts firmly in command.
Tom Latham was nine not out with Ross Taylor on two, and New Zealand facing a mountain to climb to reel in Australia's first innings total of 467.
The tourists' opening woes continued, with Jeet Raval's replacement Tom Blundell out for 15 edging a Pat Cummins delivery to wicketkeeper-captain Tim Paine.
The huge contingent of New Zealand fans in a crowd of 60,000 at the Melbourne Cricket Ground were soon groaning again when captain Kane Williamson top-edged a pull-shot to be caught by Paine for nine.
Under pressure to cement his place in Australia's middle order, South Australian scrapper Head completed his second test ton after tea and celebrated with emotion on a sun-drenched afternoon.
He was eventually dismissed for 114, smashing spin-bowling all-rounder Mitchell Santner straight to cover when looking for quick runs late in Australia's innings.
Head scored 56 in his first innings in the series-opener in Perth but was disappointed to give up his wicket with a loose drive off paceman Tim Southee.
"Last week I threw it away a little bit and then was really disappointed with that," he said. "So it's nice (to) get another opportunity."
Head combined with captain Tim Paine in a 150-run partnership that all but crushed New Zealand's hopes of forging a series-leveling victory after their 296-run loss in the pink ball test in Perth.
Their sixth-wicket stand was ended soon after tea when the tireless Neil Wagner trapped Paine lbw for 79, denying the Tasmanian skipper a maiden test hundred.
Kane Williamson's bowlers mopped up the tail for the cost of only 34 runs but the damage was already done.
New Zealand managed only one wicket from the first two sessions on Friday, placing Williamson's decision to send Australia in to bat upon winning the toss under an even harsher light.
After Australia resumed in the morning on 257 for four, paceman Wagner denied Steve Smith his first century of the home summer, dismissing the master batsman for 85 with a short ball for the third time in the series.
Smith was out parrying at a bouncer that pinged off the shoulder of his bat before being plucked out of the air with one hand by a leaping Henry Nicholls in the gully.
That was as good as it got for the Black Caps who were soon on the back foot as Head and Paine counter-attacked with vigour.
The pair marched off unbeaten at tea, having survived the whole middle session and pushed Australia to 431 for five.