New Zealand captain Stephen Fleming described his match-winning 134 against South Africa as his best ever innings.
The hosts had set New Zealand a daunting target of 307 to win, with Herschelle Gibbs contributing 143.
But Fleming led his side home to a nine-wicket win in a rain-affected match.
The skipper hammered 21 fours in 132 balls as the Kiwis took victory under the Duckworth-Lewis method.
"You wait a long time for an innings like that and it was a very important occasion for us," said Fleming.
"It means a lot and I'm happy to have led the side in that way.
"I have never played that well - especially under that amount of pressure."
New Zealand needed to win to keep alive their hopes of progress into the Super Sixes, having already lost one game and forfeited another by refusing to travel to Kenya.
Fleming admitted it had looked like a tall order after Gibbs' century in South Africa's innings.
"The pitch was good but anything over 300 is usually a pretty tough target," he said.
"We were a little disappointed with the way we bowled and that carried through lunch but we had to be positive.
"We just thought this is a last-chance knockout match, 'let's see what we can do'."
Daniel Vettori was in awe of his captain, as well as his team's battling performance under pressure.
"Stephen was awesome - that's probably the best I've seen him bat," he said.
"It's one of the best wins we have had in a long time. Everyone comes to these games to see a lot of runs and that's exactly what they got.
"There has been a lot of pressure on us in that we had to win these past two games but we've come out and done the business and it feels great.
"Now we're looking forward to the Super Six stage."