Bhuvneshwar produced a fine swing bowling display to return with impressive figures of three for 45 while his pace colleague Jasprit Bumrah (2/38)) and young leg-spinner Yuzvendra Chahal (2/36) picked up two wickets apiece as Indian bowlers came out determined after being asked to bowl.
Left-arm spinner Axar Patel (1/54) too justified the team management's decision to play him in place of Kuldeep Yadav, by removing the well settled Tom Latham.
The hosts, who lost the series opener in Mumbai, did not allow the New Zealand batsmen to settle down at the Maharashtra Cricket Association stadium.
Kumar (3-45) and Yuzvendra Chahal (2-36) and Jasprit Bumrah (2-38) were the pick of the bowlers. Electing to bat, New Zealand had a disastrous start as Kumar and Bumrah wreaked havoc by removing their first three batsmen inside the opening seven overs.
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Bhuvneshwar gave perfect start to India by removing the opening duo of Martin Guptill (11) and Colin Munro (10) quickly.
While Guptill nicked one to Mahendra Singh Dhoni behind the stumps, Williamson was trapped in front of the wicket by Bumrah with New Zealand struggling at 25 for two.
The visitors reviewed Williamson's decision but that went in vain.
Munro, who hit a towering six during his brief stay, was the next to depart as Bhuvneshwar went through his defence.
In-form Tom Latham (38) and Ross Taylor (21) too failed to repeat their last match's exploits when they conjured a 200-run stand in a winning cause.
He and Latham just managed to add 31 runs for the fourth wicket.
Latham stuck juts two fours, a cut and a pull, and partially tried to steer his side out of trouble with his trademark sweep and reverse-sweep shots.
But the southpaw's stay was cut short when he was bowled by Patel across the stumps while the batsman went for a sweep.
Chahal then took two consecutive wickets in the 44th over by dismissing Grandhomme and Adam Milne (0) to stand in chance for a hat-trick which didn't happen.
Towards the end, Mitchell Santner's 38-ball 29 and Tim Southee's unbeaten 25 helped New Zealand reach the 230-run mark.