England seemed to have achieved an insurmountable total when it reached 335-9, batting first after losing the toss, with centuries to Jonny Bairstow (138) and Joe Root (102).
England leads the five-match series 2-1 with the final game scheduled for Friday in Christchurch ahead of a two-test series later in March.
He twice received treatment and had his thigh strapped.
At 2-2, the Kiwis were in dire straits, but Taylor and Kane Williamson steadied the ship with an 84-run stand before the former came into his own.
Other players to keep an eye on are Mitchell Santner, who has been in stunning form with the bat in this series - 149 runs for once out so far - and so, with spin still his primary suit, is good value at 16/1.
Anthony Davis leaves game with apparent hip injury
As the lead shifted back and forth, Davis took the game into his hands and made several clutch shots in the game's final minutes. During their streak, Holiday is averaging 25.1 points, 4.8 rebounds, 8.6 assists, 1.3 steals and 1.4 triples on 52% shooting.
Ross Taylor smashed an unbeaten 181 runs from 147 balls and the highlight of his innings were 17 fours and six towering sixes.
New Zealand's chase then started disastrously when openers Martin Guptill and Colin Munro both went for ducks.
Ross Taylor, who missed the third game for New Zealand, is expected to be back for the fourth ODI.
Curran's late hit-out provided a welcome boost to the scoreline but also showed New Zealand's batsmen that runs are there for the taking as they chase 336.
Root brought up his century with the penultimate ball of the 47th over, but could only add another run to his total before he gloved a slow bouncer from Southee to wicketkeeper Tom Latham.
There were two late wickets for Curran, but Colin de Grandhomme's big hitting applied most of the finishing touches before Henry Nicholls settled matters with a winning six in the final over. "We knew that we wouldn't win it in the first 10 overs but you can lose it and we just tried to take it as deep as we can". Watson rewrote history books by making the highest score by an Australian batsman, beating Matthew Hayden's previous record of 181 against New Zealand and overtaking West Indies' Xavier Marshall's record number of sixes in an innings.
A New Study Shows ER Visits for Overdoses Are Skyrocketing
Public health experts say use of the overdose antidote Naloxone, coupled with a decline in opioid prescriptions may be working. But even in the smallest, most rural towns that submitted overdose data, there was a 21 percent increase in overdoses.
"It's no use going out there helter-skelter, then falling for spit and playing catch up the whole time", Taylor said.
"All four of us that got out for very little all came in and were gutted, because there was a hell of a lot of hard work that was put in to get us in that position".
"If they got to 360-370, I think it would have been an unrealistic target, especially at 2-2".
England were 267 for 1 in the 38th over when Bairstow's dismissal sparked the loss of six wickets for 21 runs.
Bowling the same two bowlers for the last seven overs of a white-ball innings, as Morgan did with Tom Curran and Woakes, is the equivalent of a barman putting seven glasses of beer in a row: it's lining them up.
Attorney General Jeff Sessions to Visit Sacramento, Make 'Major Sanctuary Jurisdiction Announcement'
Sessions planned to discuss the lawsuit Wednesday at an annual gathering of law enforcement officers in Sacramento. According to the CPOA's webpage about Legislative Day events, the event at the Sawyer is full.