Devon Conway was not out on 15 runs and Will Young was at the crease on eight runs, as New Zealand found themselves trailing by just two runs at the interval on another scorching afternoon at the iconic Wankhede Stadium.
Gill, having ridden his luck, looked well set to score a ton as India inched towards New Zealand's total after lunch, but the batsman edged spinner Ajaz Patel to Daryl Mitchell at slip and departed for a fluent 90.
Patel then removed Ravichandran Ashwin for six and finished with splendid figures of 5-103 as Akash Deep was run out, leaving Washington Sundar unbeaten on 38.
Akash put New Zealand under pressure on a tricky pitch when he castled skipper Tom Latham for one.
A late collapse on Friday meant India resumed on 86-4, and Pant eased early nerves by hitting Patel for three boundaries in the opening over before scooping one for four a little later.
Gill was handed a reprieve on 45 while looking to charge Glenn Phillips midway through the first session, when substitute Mark Chapman dropped a simple catch running in from the deep.
He then reached his seventh test half-century, as the Black Caps struggled to contain runs after missing a big chance to put pressure on the hosts.
Pant, who stepped out of his crease and hit Patel out of the park a couple of times and pulled Phillips for a four, then took a single to reach his fifty in only 36 balls, the fastest by an Indian against New Zealand.
Phillips was unfortunate to miss out again when Matt Henry dropped Pant on 53, but Ish Sodhi trapped the batsman lbw to end the fifth-wicket partnership for 96.
Ravindra Jadeja fell early in the second session for 14 when Phillips forced him to edge one to slip, while Sarfaraz Khan was caught behind for a four-ball duck off Patel.
New Zealand won the opening match in Bengaluru by eight wickets for their first test victory in India in 36 years, and wrapped up the series in Pune with a 113-run win.
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