New Zealand captain Daniel Vettori refused to single out any individuals after his side beat South Africa by 49 runs in Mirpur.
The Black Caps had Jacob Oram to thank for taking 4-39, while Nathan McCullum claimed figures of 3-29 after Jesse Ryder (83) had guided the team to 221-8 in their 50 overs.
The target appeared vulnerable as South Africa passed 100 with two wickets down, but New Zealand rallied to bowl the Proteas out for 172 and claim a shock win.
"Every single guy in the team stepped up today and I think it was the fielding that got us through," Vettori told Sky Sports.
"With a score of 221 you've got to be aggressive and in a lot of ways it's taken out of your hands, you've got to keep attacking and fortunately every time I brought a bowler on they did a good job and got wickets.
"We wanted 250, it was probably the best time to bat earlier in the day, and probably we just got a bit ahead of ourselves and got a bit aggressive.
"We scrapped through to 220 but when the batters came off they said it was a tricky wicket that would only get worse, so we thought it might be an old school game that New Zealanders are used to."
Graeme Smith's side were cruising until the dangerous AB de Villiers was run out for 35, and Vettori felt that was the wicket that turned the match.
"I think when we got de Villiers and Kallis out was when we all started to believe we could go all the way," he added.
"Around the time of the de Villiers run out was when our fielding came together and I thought that was an amazing piece of work from Martin Guptill, and I could sense from the team that was when we knew we could win.
"I think the reputation we have is that we can beat any team on a given day but consistency has avoided us a lot of the time so it's our big chance in the semi-finals to go one or two better."