In sapping heat, Labuschagne took his overnight score of 130 to 215 as Australia racked up 454 in their first innings. The illness-depleted New Zealand made a steady start in response, going to 63-0 at stumps with Tom Blundell unbeaten on 34 and stand-in captain Tom Latham 26 not out in Sydney.
Labuschagne, the world’s top Test scorer in 2019, created more history through his marathon innings of more than eight-and-a-half overs.
He now has 837 Test runs for the home season, the highest tally in a five-Test summer by any Australian, bettering Neil Harvey’s 834 of more than 60 years ago.
Australia resumed on 283-3 and while Matthew Wade fell quickly, there was far more pain in store for New Zealand, who came into this dead-rubber last Test after heavy losses in the first two, and having lost three players to a flu bug.
Labuschagne shared partnerships of 43 with Travis Head (10) and 79 with Tim Paine (35) before his 363-ball knock was ended by leg-spinner Todd Astle, who caught the in-form batsman off his own bowling.
Colin De Granhomme and Neil Wagner shared Black Caps’ bowling honours with three wickets apiece.