The left-hander smashed 18 fours off 116 balls during his eighth one-day century to help India reach its target of 259 with seven overs to spare.
Virat Kohli chipped in with 64 for the young Indian side, which was resting several senior players owing to a hectic schedule.
Earlier, new-ball bowler Shantakumaran Sreesanth bagged 4-47 as New Zealand was restricted to 258-8.
For New Zealand, Martin Guptill struck a defiant 70 off 102 balls and Scott Styris a brisk 59 off 56.
f the second one-day international between India and New Zealand in Jaipur on Wednesday:
M. Guptill c Saha b Ashwin 70
J. How c Saha b Sreesanth 5
K. Williamson b Patel 29
R. Taylor c Kohli b Pathan 15
S. Styris c Saha b Sreesanth 59
D. Vettori b Sreesanth 31
G. Hopkins not out 11
N. McCullum run out 12
K. Mills b Sreesanth 13
T. Southee not out 2
Extras: (lb5, w6) 11
Total (for eight wickets, 50 overs) 258
Fall of wickets: 1-14 (How), 2-64 (Williamson), 3-96 (Taylor), 4-161 (Guptill), 5-219 (Styris), 6-219 (Vettori), 7-242 (McCullum), 8-256 (Mills).
Bowling: Nehra 9-1-45-0, Sreesanth 9-1-47-4, Patel 8-0-34-1 (w2), Ashwin 10-0-52-1 (w1), Yuvraj 9-1-48-0 (w3), Pathan 4-0-23-1, Raina 1-0-4-0
M. Vijay b Vettori 33
G. Gambhir not out 138
V. Kohli c Taylor b McKay 64
Y. Singh not out 16
Extras: (w8) 8
Total (for two wickets, 43 overs) 259
Fall of wickets: 1-87 (Vijay), 2-203 (Kohli).
Bowling: McCullum 9-0-37-0 (w1), Mills 7-0-49-0, McKay 7-0-59-1 (w2), Styris 3-0-20-0, Vettori 8-0-32-1, Southee 5-0-33-0 (w5), Williamson 4-0-29-0
India won by eight wickets
Umpires: Nigel Llong (ENG) and Sanjay Hazare (IND)
TV umpire: Sudhir Asnani (IND)
Match referee: Roshan Mahanama (SRI)
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