The irrepressible 25-year-old had a nervous 20 minutes one run short of the milestone but a 19th four earned him his first test score in excess of 200 and a standing ovation from a packed Sydney Cricket Ground.
Labuschagne finally departed for 215, caught and bowled by spinner Todd Astle, and left the field to another huge ovation having scored 837 runs at an average of 119.57 in five home tests this season.
He faced 363 deliveries in a magnificent innings that looks to have set Australia well on their way to another victory to add to the thumping wins they enjoyed in the first two tests of the three-match series in Perth and Melbourne.
New Zealand had removed his first batting partner of the day, Matthew Wade (22), in the first over of play and the second, Travis Head (10) before lunch and made relatively short work of the tail after Labuschagne's exit.
There had been concerns that the soaring temperatures forecast for Saturday might worsen the bushfire emergency around Australia and that the blanket of acrid smoke that has covered Sydney on several occasions in recent weeks might return.
However, Labuschagne resumed his innings on 130 under bright, sunny skies, and was soon passing 150 for the third time in the five home tests against Pakistan and New Zealand.
With Australia utterly dominating those matches, their fans have had precious little drama to enjoy so it was perhaps understandable that they made the most of Labuschagne's progress through the 190s.
They were kept waiting for four overs with Labuschagne stuck on 199 and there were good-hearted boos for captain Tim Paine when he scored a single off the final ball of one to keep the strike for the next.
New Zealand pulled in the field to deny him the single and it worked for seven deliveries until he swiped at a Colin de Grandhomme delivery and got a thick edge that sent the ball racing to the boundary.
Labuschagne raced down the wicket and swiped his bat in the air in celebration before whipping off his helmet to soak in the applause of a joyous crowd basking in the sunshine.
