Skipper Suzie Bates scored 151 from 94 balls and Maddy Green posted 121 off 77 balls as their team also passed the England men's mark of 444 in the 47th over.
In Ireland's turn at bat they were rolled for 144 giving the New Zealanders a 346-run victory. The Irish wickets were spread around by the White Ferns, though Leigh Kasperek cleaned up the tail to claim 4-17 off 2.3 overs.
It's unbelievable really," Bates said following the innings.
"To set a world-record for men's and women's cricket is pretty special and it's going to take a bit to chase it down."
Bates' 10th ODI century saw her surpass the great Debbie Hockley (4,066) as the White Ferns all-time ODI leading runs scorer with 4,192 runs.
"When it happened and came over the loud speaker I did actually have a bit of a moment because you think about the hard work you have done and the people who have helped you get here.
"Debbie was a player that the team looked up to and that 2000 World Cup team was a real inspiration to us."
Bates' 94-ball innings featured a strike rate of 160.63, the second-highest in an innings of 100 or more in women's ODI cricket.
The White Ferns belted a whopping 64 fours and seven sixes, and produced century stands for the first two wickets - the first time a team has done this since 2000.
Bates and Watkin's 172-run opening stand was the sixth highest in the White Ferns history, and incredibly added to Bates' record of being involved in twenty-seven 100-run ODI partnerships for her country.
The teams will have a day off in Dublin tomorrow, before meeting again on Sunday for the second game in the three-match ODI series.