Sent in to bat, India were down 62 for 3 in the 13th over after the dismissals of Mayank Agarwal (1), captain Virat Kohli (9) and Prithvi Shaw (40) but Rahul got a useful ally in in-form Shreyas Iyer (62 off 63 deliveries) to take India to a challenging total.
Rahul, who hit nine fours and two sixes during his 113-ball innings, and Iyer stitched exactly 100 runs from 18.2 overs for the fourth wicket to revive the Indian innings.
After the end of the promising innings of Iyer, Rahul shared another 107 runs for the fifth wicket with Manish Pandey (42).
Rahul and Pandey were, however, dismissed in consecutive deliveries in the 47th over.
For New Zealand, who have already clinched the series after winning the first two matches, Hamish Bennett took four wickets for 64 runs whie Kyle Jamieson and James Neesham got a wicket apiece.
Brief Scores:
India: 296 for 7 in 50 overs (KL Rahul 112, Shreyas Iyer 62; Hamish Bennett 4/64).