After setting the Kiwis a rather improbable target of 434, the Indian bowlers, especially senior off-spinner Ravichandran Ashwin (6/132), revelled in home conditions to rip through the visiting team's line-up with more than a session to spare.
Beginning the day at a precarious 93 for four, overnight New Zealand batsmen Luke Ronchi (80) and Mitchell Santner (71) frustrated the Indian bowlers for only about 20 overs by adding 65 runs in the morning session but that only delayed the inevitable.
Ashwin (6/132) completed his fifth six-wicket haul by adding scalps of Santner and Ish Sodhi (17) and Neil Wagner (0) to his three wickets grabbed yesterday when he had become the second-fastest man to take 200-Test wickets.
Jadeja took one wicket today while Mohammed Shami, who got some reverse swing, scalped two batsmen in the morning session.
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Ashwin grabbed the remaining three wickets in the post-lunch session to complete India's victory, their 88th on home turf.
The Kiwis struggled to negotiate a slow track, which offered occasional turn and bounce but improved as the match wore on.
The visitors, chasing a mammoth 434-run target, had a daunting task at hand to bat out three full sessions on the fifth day, which has always been a big challenge for tourists in India.
(REOPENS DEL 17)
It was Ronchi, who handed India the opening when he went for a sweep slog against Jadeja and ended up handing a top-edge to Aswhin at point.
After Ronchi's departure, Santner remained solid from one end and defied the Indian bowlers for the next 10 overs with BJ Watling (18).
Together they were involved in a 36-run stand, which was broken by paceman Shami, who trapped the wicket-keeper batsman LBW.
In his next over, Shami breached the defence of Mark Craig. In a double blow to the Kiwis, Craig was also ruled out of the series due to a side strain. Jeetan Patel has been named his replacement in the squad.
Santner struck seven fours and two sixes in his 179-ball fighting knock, before an Ashwin delivery jumped and turned from outside leg, took an edge and went straight to silly point fielder Rohit Sharma.
India needed only three wickets in the second session and the in-form Ashwin took all three as he sent back Sodhi and Wagner.
Showing a renewed determination, New Zealand however
sailed easily in the middle with Guptill joined by skipper Williamson.
The only blip in Guptill innings was when he went for a lofted shot over mid-on when on 29 with Mishra nearly pulling off a spectacular catch to his wrong side.
But a smart bowling change by Dhoni who brought in Pandya, after a lengthy spell from the spinners, gave India the prized wicket of Guptill.
The Black Caps made three changes to their XI bolstering the spin attack with Ish Sodhi and Anton Devcich to go with Mitchell Santner, while wicketkeeper BJ Watling was included for the first time in the ODI series replacing Luke Ronchi.