Labuschagne, 25, finished a swelteringly hot day on 110* with Australia 4-248 at stumps, alongside Travis Head on 20*.
The century marks Labuschagne’s third at Test level, all coming in his past three innings, including two in the recent series against Pakistan.
The South Africa-born Queenslander’s rise has been dramatic, emerging during the 2019 Ashes after being a concussion substitute for Steve Smith.
He’s now become Australia’s rusted-on first drop and made the position his own.
“It’s just about riding the wave, not trying to get too high when you are going well,” Labuschagne said.
“Keeping a clear mind on the field then you just play the ball as it comes. People say you nick balls more when you are in form because you a seeing it so well so it’s about keeping a high price on decision making.”
Temperatures almost reached 40 degrees on day one, with runs coming slowly after New Zealand dismissed Joe Burns early for 9 from Colin de Grandhomme, who was returning from injury.
Neil Wagner grabbed two wickets, including a sharp caught and bowled chance to dismiss David Warner for 43, while he also had Smith out for the same score, making it 3-207.
Labuschagne and Smith fought hard during the second session, with the runs drying up, with the former captain dropped on 19, before falling in the evening session under lights.
“No hundred comes easy, but today there were patches where scoring really dried up completely and you just had to trust you would come out the other side,” Labuschagne said.
Labuschagne brought up his century with a six when on 95*.