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 (68) 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.
"Initially I just wanted to take my time when I went to bat," Rahane said. "I just wanted to play my game and whatever I've been playing since I've playing domestic cricket.
"I'm really glad that I got a hundred."
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.
"Obviously not ideal. We got ourselves into situations where if we'd taken another wicket or two we could have been chasing 100-150," New Zealand wicketkeepr BJ Watling told reporters.
"Rahane played pretty damn well and Dhoni's counter-attack hurt us.
"That partnership was probably the difference between an okay day for us and a good day for them. If we had taken a wicket there we could have been right in the hunt.
"It's a disappointing result but we've still got three days to grind it out and it looked a lot better to bat on today."
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.
"It's going to be a huge challenge," Watling added.
"We have to bat for a long time to get ourselves back in the game. Sharma is bowling really well, so is Shami, and Zaheer is really experienced and hitting some good areas and will be a challenge.
"We have to soak it up in the morning for an hour and then just bat for a long time, but I don't think there are too many demons in the wicket and it should be at is best tomorrow."
- Sports & Recreation
- Mahendra Singh Dhoni
- Zaheer Khan
- Peter Fulton