But Canada gave them a poke in the eye before eventually crumbling with the ball and slumping to an eight-wicket loss.
Canadian opener Yuvraj Samra pummelled 110 of 65 balls to help his side post 173 for four.
The Black Caps lost both openers quickly, but Glenn Phillips and Rachin Ravindra put on an unbroken stand of 146 for the third wicket to clinch the win with just under five overs to spare.
Phillips scorched 76 from 36 balls, while Ravindra quietly — hah — added 59 from 39.
It was easy enough in the end. But for a while there, Canada was on the front foot.
Samra clobbered Jimmy Neesham for three fours and a six off the last four deliveries of the powerplay as his unfancied team raced through to 50 without loss.
The 19-year-old left-hander was batting with an absence of fear and, well, respect.
He picked up a delivery from Cole McConchie and sent it over the rope as he closed in on a fourth T20 half-century.
Fellow opener Dilpreet Bajwa rotated the strike nicely.
The Canadians had an impressive platform of 75 for none at the halfway mark in their innings.
Samra sent another couple of sixes down the ground to overhaul the milestone.
Bajwa holed out for 36, having combined in a stand of 116.
Samra kept charging. He had a maiden hundred in his sights and brought it up with a bottom edge which trickled across the boundary rope.
But Canada was not doing enough at the other end. The expected flurry of runs gave way as several wickets fell late.
Canada’s tally of 173 for four felt a little light.
Canada started poorly in the field. They gave up four overthrows off a no-ball. Then a clumsy effort on the boundary rope netted the Black Caps another couple of bonus runs.
Tim Seifert could not get going. He clubbed a drive to mid-off and trudged off for six.
Finn Allen (21 from eight) followed shortly after. He spooned a leading edge to Shivam Sharma.
Ravindra helped ease some nerves in the New Zealand camp with a couple of early boundaries in his knock.
Phillips swung away consecutive boundaries to wrestle more momentum from Canada. And when Bajwa over-tossed a delivery, he dispatched it over the rope at long off. The Otago all-rounder moved into beast mode and bullied his way to a half-century from 22 balls.
From there, the game quickly slipped away from Canada.
CANADA
Y Samra c Phillips b Duffy 110 (65)
D Bajwa c Phillips b Jamieson 36 (39)
N Dhaliwal c Phillips b Henry 10 (7)
N Kirton lbw b Neesham 2 (3)
H Thaker not out 3 (3)
D Heyliger out out 8 (3)
Extras (1lb, 3w) 4
Total (for 4 wkts, 20 overs) 173
Fall:1-116, 2-153, 3-160, 4-164
Bowling: M Henry 4-0-28-1 (2w), J Duffy 4-0-25-1, K Jamieson 4-0-41-1 (1w), J Neesham 4-0-38-1, Cole McConchie 3-0-34-0, G Phillips 1-0-6-0.
NEW ZEALAND
T Seifert c Singh b Bin Zafar 6 (10)
F Allen c Sharma b Heyliger 21 (8)
R Ravindra not out 59 (39)
G Phillips not out 76 (36)
Extras (1lb, 2nb, 11w)14
Total (for 2 wkts, 15.1 overs) 176
Fall: 1-30, 2-30.
Bowling: J Singh 2.1-0-31-0, D Heyliger 4-0-42-1, S Bin Zafar 3-1-29-1, D Bajwa 2-0-26-0, A Patel 2-0-24-0, S Sharma 2-0-23-0.
Result: NZ won by eight wicket, 29 balls remaining
