India posted a competitive 179 for five at Seddon Park after being sent into bat. Opener Rohit Sharma top scored for India with a 65-run knock while skipper Virat Kohli contributed 38 runs in team’s total.
Later, skipper Kane Williamson smashed a 48-ball 95 but New Zealand faltered in the final over to take the match into the Super Over.
Needing nine runs of the last over, New Zealand lost Williamson and Ross Taylor to finish at 179 for six and tie the match.
In the Super Over, New Zealand scored 17, a target which India overwhelmed in the final ball with Rohit smashing Tim Southee for two consecutive sixes.
The fourth T20 International between the two sides will be played on Friday in Wellington.
India: 179 for 5 in 20 overs. (R Sharma 65, V Kohli 38, KL Rahul 27; Hamish Bennett 3/54.
New Zealand: 179 for 6 in 20 overs (Kane Williamson 95; Shardul Thakur 2/21).