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Australia, who won the toss and batted in the day-nighter, reached 248 for four at stumps with Labuschagne 110 not out and Travis Head unbeaten on 20.
Labuschagne batted through the final two sessions on a Perth Stadium pitch which was unresponsive before coming alive under the lights.
“It’s great to make big contributions for Australia and get us in a position where we can kick off tomorrow,” Labuschagne said.
“There were patches where scoring really dried up and you had to be patient.”
South Africa-born Labuschagne became just the ninth Australian batsman to notch three consecutive tons when he clubbed a six - just his second of his 12-test career - down the ground off spinner Mitchell Santner to add to his centuries posted against Pakistan in Brisbane and Adelaide.
He shared a 132-run third-wicket partnership with Steve Smith (43) to grab control of the contest when conditions were at their most oppressive.
Stifled by disciplined New Zealand bowling and astute field placements from captain Kane Williamson, Smith was unable to find fluency and fell when he miscued a short delivery from Neil Wagner to leg gully.
While the hosts were unchanged, New Zealand were dealt a major blow when spearhead Trent Boult failed to overcome a side strain and were further weakened when debutant quick Lockie Ferguson was forced off the field after injuring his right calf in the second session.
Yet New Zealand battled manfully and clawed their way back with the pink ball under lights, highlighted by a Tim Southee pearler to dismiss Matthew Wade for 12 shortly before the close.
An unruffled Labuschagne, however, survived through to stumps after impressively rebuilding Australia’s innings following the dismissals of their openers in the first session.
Colin de Grandhomme, New Zealand’s workhorse all-rounder, returned to the lineup after overcoming an abdominal injury and made an immediate impact with the wicket of Joe Burns for nine.
David Warner, fresh off his unbeaten 335 against Pakistan in Adelaide, fell in spectacular fashion just before the tea break for 43.
He had threatened to bat through the first session but was brilliantly dismissed by the tireless Wagner, who plucked a sharp return catch in his follow through.
Wagner said New Zealand’s bowlers showed resilience in adversity.
“The wicket was a little bit slower than we anticipated and we had to stick at it for long periods,” he said.
“I thought we stuck to our guns well and got the ball to move around at times.”
Both teams wore black armbands as a tribute to the victims of New Zealand’s White Island volcano eruption.
Most of the 19,081 spectators at the 60,000-seat stadium spent much of day one seeking refuge under the shelter of the stands with the temperature hitting 39 degrees Celsius.
New Zealand have only won one test in Australia since their sole series triumph across the Tasman Sea in 1985-86.