Josh Hazlewood impressed after taking a five-wicket haul as New Zealand were bundled out for 162 on day one of the second Test in Christchurch on Friday.
Australia, who decided to field first, reached 124 for four at stumps at Hagley Oval, with Marnus Labuschagne unbeaten on 45 and nightwatchman Nathan Lyon on one run, and trailed by only 38 runs.
Hazlewood's bowling partner Mitchell Starc snared three wickets to move past Dennis Lillee's 355 victims and jumped to fourth on Australia's all-time bowling list, behind only Shane Warne (708), Glenn McGrath (563) and Lyon (527).
New Zealand speedster Matt Henry took 3-39 to give the hosts some hope on a disappointing day.
"I think the way we started off the ball ... we could create some pressure from both ends," Henry said.
"Taking wickets is key out here .... Obviously tomorrow morning's going to be a big start for us and hopefully we can bowl well."
Playing their 100th Tests, New Zealand captain Tim Southee and Kane Williamson got a warm ovation from the sell-out crowd but their celebrations didn’t last long as Australia teared thought the home team’s batting line.
Openers Tom Latham and Will Young survived the first hour but the latter was dismissed for 14 by Starc to break the 47-run stand.
Hazlewood also bagged two wickets before lunch, dismissing Latham for 38 and Rachin Ravindra for four.
The wickets continued to tumble after the break as Hazlewood dismissed Daryl Mitchell (four) and Williamson (17).
Soon after, New Zealand lost three wickets for no run to slip to 107 for eight, with Starc removing Glenn Phillips and Scott Kuggeleijn in successive balls.
Two balls later, Blundell was also dismissed for 22 trying to pull Cameron Green.
However, a 55-run partnership by tailenders Henry and Southee helped New Zealand go past 150 before Hazlewood and Cummins wrapped up the innings.
Ben Sears, making his debut, made the occasion memorable after having Steve Smith out lbw for 11 with his third ball.
Henry cleaned up Usman Khawaja for 16 and Green for 25, with Travis Head his third scalp for 21 when he was caught behind.