The tourists needed 208 to win, but they collapsed to 79-6 in Wellington before Charlie Dean and Jones put up a record-breaking seventh-wicket stand of 130 to save the day.
With 8.4 overs remaining, England crossed the finish line behind Jones’ well-paced counterattacking performance, while Dean calmly contributed a useful supporting knock of 42.
In just her 26th game, Dean had already claimed three wickets to become the fastest woman to 50 ODI scalps.
After Bernadine Bezuidenhout and Suzie Bates shared an opening partnership of 90, the off-spinner made the first breakthrough.
