Superb bowling from Corey Anderson, who claimed his first five-wicket haul, and Hamish Bennett, back from a two-year injury break to take two for 41, had seemingly put the hosts in control as they defended their 314 total.
Chasing 315 to win, the tourists were in trouble at 146 for five. But 50 from Mahendra Singh Dhoni and R Ashwin's 65 helped them deny the Black Caps.
New Zealand were not at their best with the bat, despite knocks of 111 from Martin Guptill and 65 from Kane Williamson, and were left to ponder a night of missed opportunities - and 14 wides from their bowlers.
It was the sixth tie for both teams and kept the series alive, with New Zealand leading 2-0 with two games to play.