Acentury last-wicket stand, a top-order collapse and a comedy of errors run out conspired to put Australia in control of the first Test against New Zealand.

Having had the visitors in early trouble on the first day in Wellington, the hosts saw last-wicket pair Cameron Green and Josh Hazlewood frustrate them for much of the morning session.

They then saw their top order blown away and only some counterattacking lower down got them within 204 runs of their visitors.

Having reached his century off the penultimate ball of day one, Green added another 71 runs as he reached a Test-best 174 not out - last man Hazlewood weighing in with 22 as they took the overnight score from 279 for nine to 383.

Mitchell Starc was first to strike in the New Zealand inning as he bowled Tom Latham for five before the hosts lost talismanic batsman Kane Williamson without scoring.

Williamson, who scored seven centuries in his last seven Tests, and Will Young collided in the middle of a quick single and Marnus Labuschagne's direct hit sent the former captain packing.

Rachin Ravindra followed for a duck as he cut Hazlewood to Nathan Lyon, Young and Daryl Mitchell also departing cheaply to leave New Zealand 29-5.

Glenn Phillips hit a counterattacking 71 off 70 balls alongside Tom Blundell (33) but only Matt Henry's 42 offered much more resistance, Lyon collecting four for 34 as the hosts were dismissed for 179.

Australia opted against enforcing the follow on and lost Steve Smith without scoring off the third ball, bowled by Tim Southee.