Australia seized control of the opening Test on Friday after a miserable day for New Zealand left the hosts 217 runs adrift in Wellington and with a mountain to climb to stay in the match.

The visitors finished on 13-2 in their second innings with nightwatchman Nathan Lyon not out six and opener Usman Khawaja on five after Steve Smith and Marnus Labuschagne departed cheaply.

Tim Southee bowled Smith with his third ball, then had the out-of-form Labuschagne caught behind by Tom Blundell.

However, Southee dropped Lyon in the slips late on from Matt Henry to cap a frustrating day for New Zealand at the Basin Reserve.

Cameron Green earlier smashed an unbeaten 174 to claim only his second Test century, backing up the 114 he scored in India a year ago, as Australia raced to an imposing first-innings 383 before bowling out New Zealand for 179.

Green, 24, lit up the morning session in a superb 116-run last-wicket partnership with plucky Josh Hazlewood, who survived 62 balls for his 22.

"It was good to be at the other end and watch that sort of innings," Hazlewood said of Green's performance.

"For his career, this could be huge. To get his second hundred for Australia was outstanding."

The Australian bowlers struck early, dismissing Tom Latham (5) before Kane Williamson and Rachin Ravindra fell for ducks within the space of five balls to leave them tottering at 12-3.