The incident came in the 11th over, with England struggling to cope with a bowler-friendly pitch on 27-3.
Having been beaten by a rising delivery from Kyle Mills, Collingwood strolled out of his crease, allowing wicketkeeper Brendon McCullum to throw down his stumps.
Confusion reigned, with both umpires Asad Rauf and Darryl Harper having missed the incident at the end of the over and the latter then consulting Vettori as to whether he wanted to uphold the appeal after TV replays showed Collingwood was well out of his ground.
The incident drew memories of England's match against New Zealand 18 months ago, when Collingwood - skipper at the time - decided to uphold a run-out decision against Grant Elliott after the batsman had collided with Ryan Sidebottom pursuing a quick single at The Oval.
The Durham batsman later spoke of his regret at making the controversial call - and Vettori admitted he had to consider his position carefully before allowing Collingwood to remain at the crease.
"It was one of those situations where I had a little bit of time to think about it," he said.
The semi-final in Centurion is going to be completely different
"Under the laws of the game, it was probably out, but we have discussed the spirit of the game a lot lately and that was the basis for the decision."
"It's pretty clear-cut when something like that happens, you know what is right and what is wrong," he said.
"We definitely made the right decision and I think whether it was World Cup final, whatever, we would make the same decision.
"I just believe in karma. When we decided to keep him there I knew it was a matter of time before he got out - and I told him so next over."
New Zealand went on to record a four-wicket win over England, who made just 146 in their innings.
The victory gave them top spot in Group B and a place in the semi-finals alongside their beaten opponents, who had already qualified.
But Strauss was not enamoured with a wicket that yielded 16 wickets for less than 300 runs, saying: "I don't think it was a very good wicket for a one-day international. It was a big toss to lose.
"There's no point dwelling on it too much. The semi-final in Centurion is going to be completely different."
England will return to Centurion, where they scored 323 to beat hosts South Africa earlier in Group B, for Friday's semi-final against either Pakistan or Australia.
"We've got to remember back to that and make sure we do it again," Strauss said. "Conditions will be very different."
Analysing the defeat against the Kiwis, he said: "The batsmen needed a bit of luck to stay in. Collingwood played well, but we needed another batsman to stay there.
"If we'd got to 200 odd, it would have been a defendable total."
Kiwi skipper Vettori paid tribute to his cavalier opening batsman McCullum, who smashed four fours and three sixes in 48 from 39 balls, and Elliott, who won the man-of-the-match award after capturing a career-best 4-31.
"Brendon realised that if he could rip the guts out of England's resistance at the start of chasing that small total, we could take it away from them and it made such a difference," said Vettori.
"Elliott came back and gave us the impetus in the middle when the game started to drift from us a bit. It was a great all-round performance from our second must-win match in a row."
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