New Zealand were 111 for three at the close of play on the third day of the first Test against Australia at Wellington's Basin Reserve on Saturday, still 258 runs away from their daunting target of 369.

Spinner Glenn Phillips had earlier taken 5-45 - his first five-wicket haul in first-class cricket - as New Zealand took Australia's last six wickets for the addition of 37 runs to end the tourist's second innings on 164.

The batting was no easier for the Black Caps, however. Openers Tom Latham and Will Young both departed cheaply, while mainstay Kane Williamson had scored only nine runs when he was dismissed by spinner Nathan Lyon.

Rachin Ravindra, who reached the half century mark for the second time in his short Test career and was 56 not out at stumps, will resume on day four alongside Daryl Mitchell, who was unbeaten on 12, in a partnership worth 52 runs.

New Zealand's highest successful fourth-innings run chase was the 324 they scored against Pakistan at Christchurch in 1994. Their highest at Basin Reserve was the 285 they scored to beat Sri Lanka last year.

Australia will be looking to off-spinner Lyon to play a key role in putting the tourists 1-0 up in the two-match series that concludes with the second Test in Christchurch starting on Friday.

"Credit where credit's due, [Rachin] played very well there," said Lyon.

"But I know if we can come out here and just do our job, and put the pressure on and challenge their defence for long periods of time, hopefully we'll crack them."

As nightwatchman, Lyon had punished New Zealand for dropping him off the final ball of day two by hitting a bright 41 to push Australia from 13-2 at the start of the day to 53-3 when he was caught at square leg off Matt Henry.

Opener Usman Khawaja also departed before lunch for 28 to give Phillips his first wicket off a stumping, but Australia would have been happy at reaching the break on 113-4 with their lead already past the 300 mark.

Phillips took charge in the second session by sending back Travis Head (29) and Mitchell Marsh in successive balls before returning to dismiss Alex Carey cheaply and then finally snaring Cameron Green for 34.

It could have been better for Phillips had Australia captain Pat Cummins not twice been dropped in the deep off his bowling, but that was not going to spoil his day.

"Absolute dream come true," said Phillips. "I never thought it would be in home conditions to be able to take a five-for. I definitely thought it was going to be more on the subcontinent side of things. It's a pretty surreal sort of moment for me at the moment."

Green's 174 in a rearguard action in the first innings was largely responsible for Australia's lead, but there was to be no tail-end heroics in the second as Henry (3-36) stepped up to take the last two wickets.