Australia's top order were threatening to bat New Zealand out of the match before the first 10 overs were bowled.
On a hunch, McCullum turned to left-arm spinner Vettori in the seventh over with Michael Clarke's side 51 for one.
The 36-year-old abruptly put the brakes on the Australians and took two wickets before Trent Boult returned with a devastating five-over spell that netted five wickets, three maidens and only three runs.
Australia were dismissed for 151.
"Dan came and did his own thing and really tied it up," Boult said after the nervous one-wicket win. "He has been doing it for years now.
"He's a massive part of our team and is a pleasure to watch when he does things like that. It allows us to hang off then come back and strike at the right time."
Vettori's ability to tie up an end will be crucial to his side's chances on the small New Zealand grounds.
A stress fracture in his back more than a decade ago has nullified any torque he once had in his delivery stride and he is no longer a big turner of the ball.
But it is his ability to change flight, pace and trajectory with different arm angles that keeps the best batsmen in the world guessing and often content to push for whatever singles they can before attacking at the other end.
That kind of accuracy and parsimony creates scoreboard pressure, making him a key component in McCullum's side and a player opposing teams are wary of.

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