Rohit Sharma (147 off 138) and Virat Kohli (113 0ff 106) conjured up classy hundreds to fire India to a record 337 for six after being put into bat.
The target was imposing but New Zealand fought gamely through Colin Munro (75 off 62), Kane Williamson (64 off 84) and Tom Latham (65 off 52) before being restricted to 331 for 7 in the wake of some fine death bowling by Jasprit Bumrah.
Required to defend 15 runs in the final over, 'King of Death' Bumrah (3/47 in 10 overs) delivered yet again and conceded only eight runs in the 50th over. More importantly, he bowled an astounding 32 dot balls in his 10-over spell.
It seemed it was game on with the flying start provided left-hand opener Munro.
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He set the tone for the daunting task on the very first ball he face, flicking Bhuvneshwar Kumar for a monstrous six over midwicket.
While his opening partner Martin Guptill (10) fell cheaply again, Munro and Kane Williamson (64) kept the visitors very much in the hunt with an 109-stand off 105 balls.
The pair batted with supreme confidence on a flat surface, especially Munro who was not afraid to switch hit and charge down against the spinners. It was also a knock of substance from Williamson, who had not fired in the series until tonight.
They batted well, completing a 79-run partnership off 69 balls with their team needing 91 off the last 10 overs.
Latham carried on and played flawless to take his team on the brink of victory alongside Henry Nicholls before nerves got the better of them during the business end of the innings.
Their spectacular showing also helped India comfortably beat the previous highest score at Green Park, 303 for five that South Africa made against them two years ago.
The destructive duo was in complete control ever since Shikhar Dhawan (14) departed in the seventh over and ended up with a record breaking 230-run stand off 211 balls.
While Kohli had already hit a fine hundred in the series opener, Sharma rose to the occasion after failing in the first two games after New Zealand put the home team in.
There are not many prettier sights in cricket than seeing Sharma bat in full flow. And he did look in fine form right from the time he slashed a gentle loosener off Tim Southee over point in the first over of the match.
The Kanpur pitch, usually slow and low, played well with the ball coming on to the bat nicely. The signs were ominous for the opposition when Sharma easily picked pacer Adam Milne for a huge six over midwicket.
Kohli, on his part, began with two crisp boundaries off Southee, one through the covers and the next one a whip over midwicket.
Without taking much risk, the star pair managed to get an odd boundary in the middle overs and by the time Sharma got to his 15th ODI hundred in 33rd over, India were cruising at 183 for one.
Sharma was finding the fence more frequently than Kohli as he hammered 18 fours to go with two maximums. The two batsmen changed gears in the 36th over and the bowler at the receiving end this time was pacer Trent Boult, who leaked 17 runs in that over including four fours.
After Sharma fell to a tired shot in the 42nd over, Kohli breezed to his 32nd hundred and his second in the series, with a single off Santner.