Rahane, playing in his fifth Test, struck a classy 118 which he made from 158 deliveries with the help of 17 fours and a six as India scored 438 all out on the second day in reply to New Zealand's 192 on a Basin Reserve pitch which has considerably eased out in favour of batsmen.
Pacer Zaheer Khan then dismissed opener Peter Fulton for just one as New Zealand ended the day on 24 for one, still trailing by 222 runs with nine second innings wickets in hand.
Rahane bettered his previous highest score of 96, made in Durban against South Africa in December last. He put on a 120-run seventh wicket stand with skipper Mahendra Singh Dhoni (68 off 86 balls) as India pressed their advantage in the post-tea session with some aggressive batting.
Opener Shikhar Dhawan (98) was unlucky to miss out on a century by just two runs. Dhawan, who laid the foundation of India's best batting show of the Test series, faced 127 balls and struck 14 fours and a six.
For New Zealand, Tim Southee (3/93), Trent Boult (3/99), Neil Wagner (3/106) and James Neesham (1/62) shared the spoils among them. Corey Anderson (0/66) went wicket-less.
With three full days left, India, who lost the first Test in Auckland by 40 runs, would look to win the game and level the two-match series.