The visitors bowled out Ireland for 144 to win the match by 346 runs.
"It's unbelievable," Bates, who scored her 10th ODI century, said. "To set a world-record for men's and women's cricket is special and it's going to take a bit to chase it down."
Bates reached 4,192 ODI runs to surpass Debbie Hockley (4,066) as the all-time leading run-scorer for the New Zealand women's team.
New Zealand shattered a 21-year-old record that they previously set when they scored 455-5 against Pakistan at Christchurch in 1997. The highest ODI score in the men's game was set in 2016 when England scored 444-3 against Pakistan at Nottingham.
Amelia Kerr and debutant Jess Watkin also chipped in with half-centuries.
New Zealand were particularly harsh on Ireland leg-spinner Cara Murray who went for 119 runs in her 10 overs.
The two teams will face each other on Sunday in the second fixture of the three-match series.
(Reporting by Arjun Panchadar in Bengaluru; Editing by Christian Radnedge and Toby Davis)
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