The seventh-wicket pair uncorked an unbeaten 44-run stand in just 16 deliveries to turn a likely defeat into a four-wicket victory with just three balls to spare at Colombo's Premadasa Stadium on Thursday.
Victory for the Black Caps would have guaranteed them a passage to the semi-finals along with already qualified England, but now they'll face an anxious wait, hoping Pakistan don't hammer Sri Lanka in Pallekele on Saturday and sneak past them on net run-rate.
The odds are still on Mitch Santner's Kiwis, though, with their run-rate 1.39 compared to Pakistan's minus-0.46.
So, Pakistan must win by 64 runs or chase down Sri Lanka's total in 13.1 overs to reach the semis ahead of the Black Caps.
But while the Kiwis sit glued to the TV tomorrow - "We'll be watching," confirmed Santner -- England march on confidently to their semi in Mumbai next week, against either India or West Indies, happy they're peaking at the right time after winning all their three super-eight games.
And in Jacks, they have the current tournament MVP, as he picked up his fourth man-of-the-match award, equalling Aussie Shane Watson's achievement in 2012.
"I reckon this is the best of them," smiled Jacks, after his 2-23 with the ball that helped restrict NZ to 7-159 followed by his latest finishing masterpiece with 32no off 18 balls. "Having gone out there with the match on a knife edge, I'm over the moon."
But Jacks poured all the praise on the nerveless 21-year-old allrounder Ahmed, who made the very best of his first match of the tournament, taking 2-23 with his leggies and then hammering a decisive 19no off seven balls to help Jacks get them across the line on 6-161.
When they came together at 6-117, needing 43 off 19 balls, it had looked a forlorn hope.
"Rehan played an absolutely brilliant innings," said Jacks. "Everyone who came out on that pitch struggled straight away, but that six he hit second-ball off Glenn Phillips upped the ante and just put them on the back foot."
Indeed, the spectacular blow over long-on changed the complexion. He and Jacks had decided they had to risk it all against the offspinner and they took him for 22 in that 18th over.
Santner then leaked 16, before Jacks hit the winning runs off Matt Henry to get England home.
"Rehan did an amazing job," beamed captain Harry Brook, who had earlier delivered an even more spectacular hit that thudded into and damaged the stadium's giant screen on his way to scoring 26 off 24 balls.
Ahmed revealed afterwards that, waiting to bat, he'd been sent advice via walkie-talkie from coach Brendon McCullum: "Bat like (Virender) Sehwag..."
He followed the request to imitate the Indian great to the letter.
Phillips had earlier enjoyed a spectacular allround game, with a brisk 39 before he got cleaned up by Jacks, the key wicket of Brook and two supreme catches in the deep,
But New Zealand, having won the toss, were never really allowed by England's spinners to kick on after the fine 64-run start given to them by Tim Seifert (35 off 25) and Finn Allen (29 off 19).
Adil Rashid (2-28) was superb, with Liam Dawson (1-32), Rehan and Jacks all following his masterly spinning lead.
The only worry for Brook should be the form of Jos Buttler, who failed again, picking up his 10th T20I duck - a most unwelcome English record.
But the skipper stood by the ex-skipper, shrugging: "He's probably the best white-ball batter to ever have played the game. He's got a lot of fire in his belly and he wants to go out there and show everyone what he's made of."
