New Zealand survived a late onslaught from Dinesh Karthik and Krunal Pandya to edge India by four runs to seal the T20I series by 2-1.
With 47 needed off the last three overs, Karthik and Krunal smashed 32 off the next two overs before Tim Southee defended 15 in the last over.
"It was obviously touch-and-go there for us," said Munro whose whirlwind 40-ball 72 at the start of the match laid the platform for New Zealand's 212 for four.
Stand-in skipper Rohit Sharma won the toss and defied convention by not batting first in a series decider, saying his team preferred to chase regardless.
"It was pretty disappointing to not get over that finishing line but I thought we fought really well till the end," he said.
"We started off really well with the ODI series and we wanted to do well here with the T20."
It was a vital outing for Munro, whose position in the New Zealand side ahead of the World Cup had been in question after a string of failures in the ODI and T20 matches against India.
But he was on song from the start of the decider, charging down the track to smack Bhuvneshwar Kumar over the rope with the first ball he faced.
He and opening partner Tim Seifert raced to 80 in the eighth over before Seifert was stumped by MS Dhoni for 43.
Munro's belligerence saw him flaying the bowling with five fours and five sixes. He was removed by Kuldeep Yadav when he skied a ball to Hardik Pandya running in from long-on.
Kane Williamson (27) fell in the next over while Colin de Grandhomme chimed in with 30 off 16 to ensure New Zealand passed the critical 200 mark.
Vijay Shankar provided an equally aggressive impetus at the start after Shikhar Dhawan's early dismissal and the visitors were up at the required run rate through the first half of their innings. But wickets after after regular intervals meant they were never able to establish partnerships.
Rishabh Pant raced to 28 off 12 before he became debutant Blair Tickner's first victim. Sharma made 38, Hardik Pandya's (21) while Dhoni could only make two.