The Kiwis, resuming the final day on 73 for 4, chasing 213, suffered an early blow when nightwatchman Paul Wiseman was trapped lbw by Javagal Srinath off the fourth ball of the morning. However, McMillan and all- rounder Cairns steadied the ship to put their side 1-0 up in the three- Test series.
Cairns was out for 61 and Dion Nash hit the winning boundary off Srinath.
Cairns was relieved to contribute after failing to take a wicket in either innings and scoring a second-ball duck in the first innings. "I was nervous for the first time in a long while and it was good to have to play with some real pressure on," he said.
The New Zealand captain, Stephen Fleming, said the match had been the most exhausting of his career. "It is the most mentally demanding Test match I've been involved in. You would go home every night mentally knackered," he said.
India's captain Mohammad Azharuddin said dropped catches cost his side dearly and he called for a radical change before the final Test, which starts in Hamilton on Saturday.
Final day; India won toss
INDIA - First Innings 208 (M A Azharuddin 103no; S B Doull 7 for 65).
NEW ZEALAND - First Innings 352 (D J Nash 89no, D L Vettori 57, N J Astle 56; A Kumble 4 for 83).
INDIA - Second innings 356 (S R Tendulkar 113).
NEW ZEALAND - Second innings
(Overnight: 73 for 4)
M D Bell c Dravid b Srinath 0
M J Horne lbw b Kumble 31
*S P Fleming b Kumble 17
N J Astle retired hurt 1
C D McMillan not out 74
A C Parore run out 1
P J Wiseman lbw b Srinath 0
C L Cairns c Jadeja b Srinath 61
D J Nash not out 4
Extras (b9, lb9, nb8) 26
Total (for 6) 215
Fall (cont): 15-74, 6-211.
Did not bat: D L Vettori, S B Doull.
Bowling: Srinath 19.3-1-82-3 (nb8); Venkatesh Prasad 10-3-26-0; Kumble 23-6-70-2; Singh 5-1-11-0; Tendulkar 3-0-8-0.
Umpires: E A Nicholls (West Indies) and E A Watkin (New Zealand).Reuse content