Earlier, centurions Virat Kohli and Rohit Sharma featured in a mammoth 230-run stand to help the hosts post 337-6 after New Zealand, wary of the dew factor later in the evening, elected to field at Kanpur's Green Park Stadium.
New Zealand lost opener Martin Guptill early in their reply but Colin Munro smashed three sixes in his blistering 75 and Kane Williamson made a fluent 64 to help them overcome the early loss.
Wristspinner Yuzvendra Chahal ended the 109-run partnership, dismissing both the batsmen but Tom Latham refused to throw in the towel.
Latham and Ross Taylor had engineered New Zealand's successful in the series opener in Mumbai and they looked determined to reprised the role.
Bumrah (3-47) poured cold water on their plans, however, by first dismissing Taylor for 39 and then running out Latham, who made 65, in the 48th over of the New Zealand innings.
Put into bat, India lost Shikhar Dhawan (14) early but New Zealand had to toil in the subsequent 35 overs as Kohli and Sharma became the first ODI pair to star in four double-century partnerships.
Sharma batted with characteristic elegance to score 147 off 138 balls. His 15th one-day century was studded with 18 boundaries and a couple of sixes before he fell in the 42nd over.
Kohli was silky smooth at the other end as the India captain became the fastest batsman to complete 9,000 ODI runs, achieving the feat in 194 innings.
The right-hander made 113 off 106 balls, with nine boundaries and a six in his 32nd one-day century.
The teams will next square off in a three-match Twenty20 series beginning in New Delhi on Wednesday.
(Reporting by Amlan Chakraborty in New Delhi; editing by Clare Fallon)
