After being put in to bat, New Zealand posted a total of 207 and took wickets at a consistent rate early on to leave England reeling at 79-6.
England were eventually rescued by Jones (92 not out) and Dean (42 not out), who guided the visitors over the finish line with their assured partnership.
The unbeaten 130-run stand between the pair bettered the previous record of 122 between India's Sneh Rana and Pooja Vastrakar against Pakistan in a 2022 Women's World Cup match at Mount Maunganui.
"Me and Deano were constantly saying, 'one ball at a time' and 'just react', which kept us in the moment. I thought we played with freedom and did what we set out to," Jones told reporters.
"For that to pay off, (this innings) ranks quite highly I'd say."
The teams meet in the second ODI at Seddon Park in Hamilton, New Zealand on Thursday.
