Vettori, 36, was handed the ball in the 11th over after Sri Lanka had made a promising start in pursuit of New Zealand's 331 for six at Hagley Oval.
In his second over, with Sri Lanka on 67 for no wicket, Vettori deceived Tillakaratne Dilshan into lobbing a simple return catch. He bowled one more over before captain Brendon McCullum decided to take him out of the attack.
With the arrival of Mahela Jayawardene at the crease, McCullum called on his tall left-armer again, aware that Vettori had notched notable triumphs over the classy Sri Lanka in the past.
Jaywardene, one of a trio along with Dilshan and Kumar Sangakkara with the class and ability to play a match-winning innings, was noticeably wary against Vettori's guile and variations of pace.
But after lasting only four balls without scoring he pushed forward at another good length delivery, the ball caught the edge, and Luke Ronchi behind the stumps leaped in triumph. The dismissal of Sangakkara in the next over for 39 effectively spelt the end of Sri Lanka's hopes.
"It was a plan," man-of-the-match Corey Anderson told a news conference.
"Dan's got him out numerous times and it obviously paid off for us today again. He's just a clever bowler. It's one of those things, you'd like him to bowl more than 10 but he can't."
Vettori's 10 overs against an Asian side brought up on a diet of spin cost only 34 runs and ensured, if there had been any doubt, that he will now be an automatic choice ahead of Nathan McCullum for the spinner's spot.
McCullum, like his brother, is a brilliant fielder but Vettori showed he can still play a full part in the field with a fine, tumbling catch to dismiss Sri Lanka captain Angelo Mathews.
He accepted the congratulations of his team mates without a flicker of emotion and Anderson was effusive in his praise afterwards.
"He is just so good. He's played a lot of cricket," Anderson said.

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