They defeated the Kiwis by 5 wickets to send them back home from the Group A of the tournament. They now depend upon the results of England Vs Australia tomorrow (June 10).
If England beats Australia, Bangladesh go through to the semis as the second team from the group.
In today's match, chasing a total of 266 runs, Bangladesh lost 4 wickets for just 33 runs but a brilliant partnership between Shakib Al Hasan and Mahmudullah Riyad sealed the fate of the match in their favour.
Here are the highlights from the post-match presentation ceremony:
What did the losing captain Kane Williamson say?
"To be fair, on that surface we felt it was a scrappy total to get. If we bowled well, we could make it difficult. The boys were outstanding with the new ball.
"But we left a few runs out there. A long way from a perfect performance today. Credit to the way Bangladesh played.
"That partnership from Shakib and Mahmudullah was simply superb. Something around 285 would have been very competitive."
What did winning skipper Mashrafe Mortaza say?
"It is a great feeling. Both times I have been here (Cardiff). I still remember 2005 against Australia and now against New Zealand. Overall, we are very much satisfied. First match we were not up to the mark with the ball.
"Today, the bowlers hit the right areas. Mosaddek's (Hossain) three wickets was crucial. Neesham and Corey got out to him in New Zealand. Once the left-hander came, I went to the offspinner. The way Shakib and Mahmudullah batted was out of the world for me. We had the confidence once we beat New Zealand in Ireland. We are feeling great right now."
What did centurion Mahmudullah Riyad say?
"Tamim batted superbly in this tournament. He got a hundred and almost a hundred against Australia. Losing him early on was quite a shock but Shakib and I had a good partnership.
"We were just looking for bad balls and kept hitting them away and keep looking for gaps to take singles."
What did the Man-of-the-match Shakib Al Hasan had to say?
"As Mahmudullah said, we did not talk much. We just said 'keep going'. We did not think of the target and just wanted to bat 40 overs and see where we were.
"The good thing was that we handled the swinging ball well and when there were balls to hit, we hit them.
"Winning a match in an ICC tournament is a big thing and we have come a long way in the last two years. From here on we can only go forward."