Australia were in a comfortable position after they bowled out New Zealand for 179 in the first Test on Friday's second day.
Cameron Green notched up a brilliant 174 not out to help Australia post 383 in their first innings.
The Black Caps were bowled out cheaply with Glenn Phillips's aggressive 71 saving them from complete capitulation in front of a packed crowd at Wellington's Basin Reserve.
Australia didn’t enforce the follow-on but the wickets kept tumbling with skipper Tim Southee sending back Steve Smith and Marnus Labuschagne without a major dent on the scoreboard.
Nightwatchman Nathan Lyon’s catch was spilled by Southee in the slips off the last ball of the day and will resume on six not out along with Usman Khawaja, who was unbeaten on five. Australia are 13-2 with a lead of 217 runs.
New Zealand, eyeing only a second win over Australia in 24 Tests this century, were looking to quickly remove the final Australian wicket but Green and Josh Hazlewood fought back for two hours.
All-rounder Green, who had reached the century yesterday, continued to attack, scoring 23 fours and smashing five sixes in a marathon 275-ball innings.
Hazlewood added 22 off 62 balls at the other end as the pair combined for 116 runs before seamer Matt Henry dismissed the Australian paceman to bag his second Test five-wicket haul with figures of 5-70.
In reply, the home side were quickly reduced to 12-3. Tom Latham departed for five and two balls later Kane Williamson was run out for a duck after colliding with his batting partner Will Young.
Rachin Ravindra was also sent back three balls later with zero runs to his name after a good Nathan Lyon catch off the bowling of Hazlewood.
Australia skipper Pat Cummins also joined the party when he dismissed Daryl Mitchell and Mitchell Marsh ended Young's innings to leave the hosts on 29-5.
Phillips and Tom Blundell provided some stability with a partnership of 84 but Lyon (4-43) ended their resistance when he had the latter caught for 33 off an inside edge.
Two balls later, Scott Kuggeleijn became the off spinner's second victim and the home side were again reeling at 113-7.
Hazlewood finally accounted for Phillips with a short delivery and Lyon stopped Henry's pugnacious knock on 42 to wrap up the innings.
The second and final Test in Christchurch begins on March 8.