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.
Image: India’s Ajinkya Rahane celebrates his first test century against New Zealand on the second day of the second cricket test in Wellington, New Zealand, Saturday, Feb. 15, 2014.