Matt Henry claimed a seven-wicket haul to restrict Australia before Tom Latham and Kane Williamson struck half-centuries to continue New Zealand’s stirring fightback in the second Test at Hagley Oval.

But Williamson fell late on day two for 51 after succumbing to the first ball of a new spell from Pat Cummins, dragging a delivery onto his stumps that had deceptively decked back.

Just before stumps, Latham edged a delivery from Josh Hazlewood that shaped away only for wicketkeeper Alex Carey to spill a chance after diving low down in front of Usman Khawaja at first slip.

Latham finished unbeaten on 65 from 154 balls in his highest Test score against Australia. He entered averaging just under 28 against them compared to 40 overall. Rachin Ravindra had some anxious moments, but fought hard to reach 11 not out with New Zealand leading by 40 runs.

As was expected ahead of the match, the pitch appeared to be flattening out, but there was still enough movement and bounce for the seamers to exploit. Australia used six bowlers with Cummins and Hazlewood, who was the standout with a five-wicket haul in the first innings, looking threatening before the close.

New Zealand’s batting has been under the microscope having failed to reach 200 runs in their three previous innings in the series. After opener Will Young fell early to Mitchell Starc, Williamson and Latham erased New Zealand’s 94-run first innings deficit with a 105-run partnership.

Williamson, in his 100th Test, played elegantly and unfurled trademark drives to reach his half-century off 105 balls. Having made just 26 runs in the series, Williamson was in a determined mood and looked set for the long haul having converted his previous eight fifties into centuries.

There was extra fuel for Williamson, whose career average of 37 against Australia is modest compared to his overall mark of 55. But he was left in despair after falling to Cummins following a rare sedate period of a play in what has thoroughly been a bowler-dominated series.

Relatively quiet in the series with just two wickets previously, Cummins produced a hostile spell late in the day amid cloudy conditions. But Latham and Ravindra held firm to continue New Zealand’s turnaround after they made just 162 in the first innings.

Henry dominated the earlier part of the day to claw New Zealand back in the contest and restrict Australia to 256. His figures of 7 for 67 from 23 overs were the second best by a New Zealand bowler against Australia and only behind Sir Richard Hadlee’s famous 9 for 52 at the Gabba in 1985. It was Henry’s second consecutive five-wicket haul after being a shining light in New Zealand’s hefty first Test defeat.

Australia’s stuttering batting-order once again weren’t able to muster a formidable effort and let their stranglehold slip, with Marnus Labuschagne the only batter to score more than 30 runs in the innings. He superbly anchored the innings to emerge from a form slump with 90 off 147 balls.

Labuschagne, who has only made two of his 11 hundreds away from Australia, had endured lean form over the last 12 months, and has seen his Test average drop below 50 having once soared above 60. He had suffered four consecutive single digit innings before this match.

Other than Labuschagne, a number of Australia’s batters could not go on with starts although cameos from Cummins, Starc and Nathan Lyon lifted them to a handy lead.

New Zealand were frustrated initially by Lyon, the nightwatcher, who underlined his form with 20 before edging Henry to Daryl Mitchell, who made amends after dropping a chance earlier in the day. Henry continued his excellent series when he trapped Mitchell Marsh on the crease in a decision overturned on the DRS when captain Tim Southee decided to review at the last second.

It was Marsh’s second consecutive duck, while Carey’s struggles against spin continued when he gifted Glenn Phillips – who had been brought into the attack in an inspired move by Southee – a wicket after a poorly executed paddle stroke on 14.

With Josh Inglis breathing down his neck, Carey’s place in the team will further be in the spotlight having only made two half-centuries in his last 18 innings.

Labuschagne held the innings together and his determined work in the nets in the lead-up paid off with well-executed plans evident. He made an emphasis to counter the movement by getting across the stumps and hitting into his favoured on-side

But Labuschagne’s tactics of walking down the pitch, especially to Henry, raised the eyebrows of the umpires who got together to discuss whether he was moving into the protected area of the pitch.

Labuschagne’s bid for his first century since the Ashes Test in Manchester last year was cut short by a spectacular catch from Phillips at gully after leaping high to his right on the last ball before lunch.