Chasing a mammoth target, New Zealand lost their top order inside five overs and were bundled out for 66 in 12.1 overs.
Gill hammered an unbeaten 126 off 63 balls to power India to 234-4, their highest T20 total against New Zealand, vindicating skipper Hardik Pandya's decision to bat first in the decider.
India lost opener Ishan Kishan in the second over but what followed was batting carnage from Gill.
The elegant right-hander belted 12 fours and seven sixes and went on to register the highest score by an Indian batter in T20 Internationals.
Rahul Tripathi made a quickfire 44 and Pandya contributed 30 but the day belonged to Gill, who has now scored a century in all three formats in international cricket.
When New Zealand began their chase, Pandya (4-16) removed Finn Allen for three in his first over and Glenn Phillips in his second.
In between, Arshdeep Singh took two wickets in an over to further jolt New Zealand who slumped to 21-5 after Michael Bracewell lost his middle stump to Umran Malik's express pace.
Shivam Mavi dismissed Mitchell Santner and Ish Sodhi in his first over to tighten the noose and Daryl Mitchell's defiant 35 could not prevent India from registering their biggest T20 victory in terms of runs.
The hosts had swept the preceding three-match one-day series between the sides.
