Their 140-run stand boosted the hosts from 85 for 4 to 323 for 6 by the end of the fourth day, an overall lead of 273. That total puts the match virtually beyond India, who must win to tie the series at 1-1.
In losing four wickets, New Zealand scored only 44 in the two hours before lunch but the innings was brought to life by McMillan and Parore, who occupied the crease throughout the second session. McMillan scored 84 and Parore 50, but both were out with the total on 225.
McMillan, driving with power and punishing anything short, faced 102 balls and hit 13 fours. Parore's 50 came off 120 balls with six fours. Chris Cairns and Dion Nash carried on the good work, adding 98.
Anshuman Gaekwad, the Indian coach, admitted: "It will be difficult for us to win now."
Fourth day; India won toss
NEW ZEALAND - First Innings 366 (M J Horne 67, R G Twose 87; J.Srinath 5-95).
INDIA - First Innings 416 (R S Dravid 190, J Srinath 76, S R Tendulkar 67; C L Cairns 4-107).
NEW ZEALAND - Second Innings
(Overnight: 45 for 0)
M D Bell lbw b Tendulkar 25
M J Horne c Mongia b Srinath 26
*S P Fleming b Prasad 18
R G Twose lbw b Tendulkar 4
C D McMillan c Mongia b Singh 84
A C Parore c Singh b Kumble 50
C L Cairns not out 52
D J Nash not out 46
Extras (b8 lb6 w1 nb3) 18
Total (for 6) 323
Fall: 1-46, 2-69, 3-76, 4-85, 5-225, 6-225.
To bat: D L Vettori, P J Wiseman, S B Doull.
Bowling: Prasad 27-8-55-1; Singh 15-2-77-1 (w1); Srinath 20-6-62-1 (nb3); Kumble 34-10-82-1; Tendulkar 7-0-30-2; Ganguly 3-1-3-0.
Umpires: D B Cowie (NZ) and R E Koertzen (SA).Reuse content