Match-winner Shami had no issues warming the bench for India
Shami watched from the sidelines as India won each of their first four matches and the right-arm bowler would have sat out again but for an ankle injury to Hardik Pandya, which forced the team to recall Shami.
Shami responded by claiming a wicket with his first delivery of the tournament and was on the verge of a hat-trick after dismissing Mitchell Santner and Matt Henry off successive deliveries.
While a second ODI World Cup hat-trick for him did not materialise, Shami's 5-54 helped India to bowl out New Zealand for 273 and set up their four-wicket victory with two overs to spare.
It also earned him the player-of-the-match award.
"Obviously, the start was important and getting a wicket first ball gave me plenty of confidence," Shami said, adding that he had been fine watching Jasprit Bumrah and Mohammed Siraj share pace-bowling duty with all-rounder Pandya.
"It's not too hard if your team is doing well," said the seamer.
"They are your teammates and if they are doing well then you should be supporting them.
"If it's in the team's interest, I'm okay with it."
Skipper Rohit Sharma was pleased with how Shami made an immediate impact with the ball.
"Shami took his opportunity with both hands," Rohit said.
"He is a class player, with so much experience and I am very happy for him."
India are now the only unbeaten team in the tournament, leading the race for the four semi-final berths, followed by New Zealand, who suffered their first defeat in Dharamsala.
Rohit's team play England in Lucknow next Sunday, a day after New Zealand play Australia in Dharamsala.
