New Zealand took a 65-run lead after Australia scored 559-9 declared.
Taylor's total surpassed that of England's R.E. Foster, who scored 287 against Australia in Sydney in 1903, and he fell just short of becoming only the second batsman to score a triple century against Australia after Len Hutton, who did it in England in 1938.
Taylor's innings is the third highest by a New Zealand batsman. He batted for nine and half hours, facing 374 balls and hitting 43 boundaries.
Resuming the day on 510-6, New Zealand was soon reduced to 587-9 before No.11 Trent Boult helped Taylor guide the side past 600 for the first time against Australia.
Left arm swing bowler Mitchell Starc took 4-119 while off-spinner Nathan Lyon, who claimed the prized scalp of Taylor, took 3-107.
The New Zealand total is its fifth highest in all test matches.
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