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).
The hosts chased down the target in 49.3 overs.
"It was nice to be there at the end", Taylor said.
The final ODI takes place in Christchurch on Friday at 22:00 GMT.
It was just like old times for Bairstow and Root, who have known each other since their early teens. Since then, he has averaged 65.50 in one-day cricket, with four centuries and nine half-centuries to his name.
The New Zealand batsman missed the third ODI loss to the English in Wellington after suffering a quad injury during the second ODI loss in Tauranga.
New Zealand's chase then started disastrously when openers Martin Guptill and Colin Munro both went for ducks.
Alongside Williamson, Taylor steadied the innings.
Anyone who doubted Ross Taylor's importance to the Black Caps should be scoffing their face with humble pie.More news: Manchester United back to 2nd spot on EPL table
Ross Taylor struck his career best ODI score with an unbeaten 181. Unable to run, Taylor freed his arms.
When Latham fell, miscuing Tom Curran to backward point, de Grandhomme picked up the mantle. He hit Chris Woakes for a six and a four in the next over and the game was as good as done.
It was not that simple. England then exerted itself and shut down the run flow for more than an over, tipping the balance of the match in its favour. As a result, a significant drop in his six-hitting frequency and he did not even hit one six in his previous 21 ODI innings where he scored 950 runs.
Bairstow was brutal on the New Zealand attack, and perhaps only spinner Ish Sodhi will be keen to re-watch his performance after taking 4-58.
But Santner was culpable when he put down an easier chance at extra-cover off Trent Boult to reprieve Bairstow on 74.
This was his second century in the series. He may have reached three figures quicker had he not struggled for the strike.
His knock gave the Kiwis victory by five wickets with three deliveries remaining as they ultimately surpassed England's total of 335-9 with a bit to spare. It felt as though England were light on runs - and Taylor proved it in some style. He was superb. But England lost this game.
He also became the 2nd highest run getter (7,267) for New Zealand in ODIs.
Ex-England batsman James Taylor: "It looked like complacency - nearly arrogance - from England, to go hell for leather straight up in your innings".
England will no doubt look back and wonder how the match got away considering New Zealand still needed 141 runs from the last 15 overs. He has been batting like this all year. "It was an outstanding partnership with him and Tom Latham".