After a stunning last over where England got 14 runs, the game went to a historic super over.
Stokes and Buttler came on to face Trent Boult in the super over and hit 15 from the six pressure balls.
Jofra Archer bowled England’s over and sealed the win.
The hosts were set a modest 242 target and were saved by Jos Buttler and Ben Stokes’ 105-run fifth wicket partnership saved the match as Stokes powered England to a tie.
Stokes sliced in the air from Boult's first delivery but he and Buttler ran hard to collect three before the latter claimed a single.
In the super over, Stokes sliced in the air from Boult's first delivery but he and Buttler ran hard to collect three before the latter claimed a single.
Stokes then slog swept Boult for four and then collected a single. Boult's next ball was a yorker but Buttler was still able to get back for a couple before creaming a shot into the leg-side for four.
England, therefore, left New Zealand needing 16 to win the World Cup thanks to Stokes making eight and Buttler seven from three balls apiece.
Jimmy Neesham and Martin Guptill came out to face Jofra Archer, and nobody could have predicted what came next.
Neesham stretched but failed to make contact with the first delivery, signalled a wide, before he and Guptill ran a couple after shovelling into the off-side.
Neesham was well back in his crease when he walloped Archer for a maximum to leave the Kiwis needing seven off four. A misfield from Roy at deep midwicket then allowed Neesham and Guptill to come back for two.
A quick single was taken from the penultimate ball, Archer opting to keep the ball in his hand rather than risk overthrows.
Two were needed from the final ball. Guptill flicked the last ball to deep mid-wicket and tried for the second, but England quickly got the ball to Buttler and the run out was complete. The super over was tied and England were winners having scored more boundaries.
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