17 overs into the chase and it appeared the small total was plenty with the world number two side struggling at 79 for six.
Tammy Beaumont was removed for a duck in the first over by Jess Kerr, who also dismissed England skipper Heather Knight in the ninth over.
Within four overs the match turned New Zealand’s way as the wickets continued. Maia Bouchier, star of the fourth T20, fell to Lea Tahuhu for 31, Nat Sciver-Brunt was run out by Hannah Rowe going for two following a mis-field before Amelia Kerr trapped Alice Capsey LBW for a duck and tricked Danni Wyatt with a wrong-un, leaving England needing another 129 to win.
But New Zealand didn’t take another wicket as Jones and Dean pulled off a remarkable recovery with 52 balls remaining.
Player of the match Jones finished just two shy of her career-best and eight short of a maiden ODI ton.
“Fairly highly,” Jones said after the match in being asked where she ranked the innings in her career. “I’ve done quite a bit of work on the mindset going into run chases. It’s an area that I felt I could do better in. So pleased that work paid off today.”
Amelia Kerr said either 20 more runs or one more wicket could have changed her side’s fortunes.
“I thought Suzie was outstanding and set the platform there for us but we lost wickets in clumps through the middle. I thought Kate Cross bowled very well on that wicket. There was enough in it if you bowled a good length and we didn’t have any answers to their changes of pace and variation. If we can scrap a little more to get to 220-230, I thought after the start we were in a position to potentially get 250 plus. But you look at the bowling side of things, one more wicket and we could have defended 200.
“Unfortunately we couldn’t get that one wicket. I thought they both batted incredibly,” the skipper added.