India, who won the preceding one-day series against New Zealand, wobbled early in their chase and eventually managed 156-7 despite skipper Virat Kohli's defiant 65.
Thiruvananthapuram hosts the decider on Tuesday.
Munro and Martin Guptill gave New Zealand a flying start after skipper Kane Williamson opted to bat at the Saurashtra Cricket Association Stadium in Rajkot.
The openers tore into the Indian attack during their 105-run stand in 11 overs.
Guptill clobbered three sixes in his breezy 45 before being dismissed by Yuzvendra Chahal.
Munro brought up his fifty in 26 balls and was on 79 when Chahal dropped him at deep cover. The opener took 54 balls to complete his second Twenty20 century.
Debutant Mohammed Siraj claimed his maiden international wicket when the paceman dismissed rival captain Kane Williamson for 12.
India's reply got off to a contrasting start with the hosts losing both their openers inside the first two overs of their innings.
Kohli and Shreyas Iyer raised 54 runs for the third wicket before Munro struck, dismissing Iyer for 23.
Mahendra Singh Dhoni (49) struck three sixes but the mounting run rate prompted Kohli to try to accelerate and he perished in the process.
Paceman Trent Boult claimed 4-34, while spinners Ish Sodhi and Mitchell Santner also bowled tidy overs.
(Reporting by Amlan Chakraborty in New Delhi; editing by Clare Fallon)
