The hosts are still 222 runs behind India's first innings of 438 and face an uphill battle to save the match after opener Peter Fulton was trapped lbw for one by Zaheer Khan in the second over of their second innings.
The under pressure Hamish Rutherford was on 18 while Kane Williamson was on four at stumps.
Rahane had anchored the visitors' innings with a compact approach in holding up his end as he featured in productive partnerships with Virat Kohli (38) and Mahendra Singh Dhoni (64) to help establish what should be a match-winning lead.
He pulled Corey Anderson to the midwicket fence for his 15th boundary and raised his arms in triumph as his team mates all stood and applauded. His previous best was 96 against South Africa in Durban.
The 25-year-old opened up after he achieved the milestone, belting two more boundaries in the over and then hitting a six shortly after before he fell to a brilliant one-handed diving catch by Trent Boult at deep cover.
The hosts were dismissed for 192 on the first day and will need to bat until at least the fourth day to ensure they can salvage a draw to win the two-match series.
"We just didn't get it in the areas we needed and didn't bowl enough good balls," Boult told Radio Sport after he had taken three of India's wickets.
"We struggled with a bit of both (line and length) and enough pressure wasn't built from both ends.
"We are a little bit disappointed as a group and now we're in a pretty tough situation."
India had resumed on 100 for two and patiently built their innings throughout the day even though they had lost three wickets in quick succession in the first session.
Nightwatchman Ishant Sharma, who took career-best figures of 6-51 in New Zealand's innings, ensured his batsmen were not exposed early in the day and was dismissed for 26, Shikhar Dhawan fell two runs short of his third century, while Rohit Sharma played on for a duck.
Kohli was the only wicket to fall in the afternoon after a 63-run partnership with Rahane, who then combined for a 120-run stand with Dhoni.
The India captain upped the run rate after tea, which allowed the visitors to rattle past 400 late in the session.
New Zealand's second innings began terribly with Fulton not offering a shot to a Zaheer delivery and was trapped in front to leave them in dire straits.
New Zealand hold a 1-0 lead in the two-match series after their 40-run victory at Eden Park in the first game and will need to bat well into the fourth day to at least try to salvage a draw and seal the series.
Boult insisted that was possible.
"The wicket has definitely flattened out and is a pretty good batting surface now. I don't think there are too many demons out there," he said.
"We know that they will come hard at us in the first hour and if we can knuckle down then I'm sure there is a lot of belief in the room that we can bat a good day and a lot more."