Australia captain Pat Cummins heaped praise on team-mates Nathan Lyon and Cameron Green on Sunday for match-winning performances as his side secured a 172-run triumph over New Zealand in the first Test.

Lyon spun the visitors to victory in the morning session on day four in Wellington, taking six wickets as New Zealand crumbled to 196 all out.

New Zealand lost their last seven wickets before lunch for 70 runs, with four falling to off-spinner Lyon, who finished with figures of 6-65 off 27 overs and 10-108 in the match.

The 36-year-old capitalised on spin-friendly Basin Reserve conditions and some meek batting from New Zealand, who began the day on 111-3 needing an unlikely 258 more runs to win.

Green's career-high unbeaten 174 on day one rescued Australia from 89-4, having been put into bat, to reach 383 and set up a decisive 204-run first-innings lead.

It gave Green the nod over Lyon as man of the match and Cummins said that was a fair outcome.

"Cam was amazing, he was really the difference in the end," Cummins said.

"I thought the way he went about it, with that intent, really put the pressure back on the bowlers on day one.

"There was as much bounce as I've seen in any wicket for a long time but thankfully it spun which, with Nathan in our side, is always a pretty good thing."

New Zealand pace bowler Will O'Rourke is a doubt for the second and final Test starting in Christchurch on Friday after leaving the field with a tight hamstring on day three.

Captain Tim Southee said he wouldn't rule out a shock recall for veteran pace bowler Neil Wagner, who retired last week.

The 37-year-old had been named in New Zealand's squad, but tearfully announced his retirement after being left out of the first Test side, ending a 64-Test, 260-wicket career.

Southee ruled out calling up Trent Boult because he has only been playing white ball cricket of late, but was less adamant when asked about Wagner.

"Obviously the Test match has only just finished so we'll see how Will scrubs up and we'll go from there," Southee said.

Cummins said Australia would be prepared if Wagner returned. "It'd be the world's shortest retirement," he said of the short-ball specialist. "It'd be good to see his high energy."

Southee hailed Glenn Phillips after the all-rounder top scored with 71 in the first innings and claimed career-best figures of 5-45 with his part-time off-spin as Australia were dismissed for 164 in the second.

"Glenn's still new to Test cricket and new to bowling, and he's doing a great job," Southee said of the 27-year-old.

Southee and batsman Kane Williamson will both play their 100th Test at Hagley Oval in Christchurch.

The final morning's capitulation began in the seventh over when Lyon claimed the key wicket of Rachin Ravindra for 59.

Ravindra had only added three to his overnight score when he failed to keep a cut shot down and was caught by Cameron Green at point.

Tom Blundell was caught close in by Travis Head without scoring in the same over and Glenn Phillips was trapped leg before by Lyon for one soon afterwards, to expose the tail.

Scott Kuggeleijn struck 26 off 28 balls before he failed to control a short ball from Green to be caught by wicketkeeper Alex Carey and Matt Henry fell for 14, caught at slip by Steve Smith off Josh Hazlewood.

Southee became Lyon's sixth victim before Daryl Mitchell was the last wicket to fall, for 38, caught and bowled by Hazlewood.