New Zealand have halted Australia's charge to claim victory in the first Test of their series with a resilient display on day four at the GABBA.

Steve Smith declared the Baggy Greens' second innings on 264-4, leaving the Kiwis a mammoth 504 runs to chase on the final two days of the match.

Openers Tom Latham and Martin Guptill fended off the challenge of Mitchell Starc and Mitchell Johnson with the new ball as they saw their side through the opening 20 overs.

However, Latham was the first victim of the innings when he fell lbw to Starc for 29 to end the opening partnership at 44.

First-innings centurion Kane Williamson arrived at the crease and continued the Kiwis' stoic resistance.

Williamson and Guptill took their partnership into the afternoon session and reached 50 together before Guptill was out for 23 off 117 deliveries as he was dismissed by Nathan Lyon.

Williamson continued to defy the Aussies and reached his second half-century of the match off 55 balls, but was then out for 59 as Lyon trapped him in front of his stumps.

Ross Taylor and Brendon McCullum made it through to tea unscathed before rain wiped out the final session of the day with New Zealand on 142-3, 362 runs shy of an unlikely victory.