England posted an impressive 172 for six having being asked to bat first, but saw the game taken away from them in the blink of an eye in a reply that lasted just 5.2 overs - just over the maximum needed to constitute a game - before thunder, lightning and heavy rain engulfed the stadium.
Both teams had no option but to run for shelter as the covers came on, but Stuart Broad later insisted the decision to remove the players should have been taken earlier on safety grounds after the ground had been struck several times by lightning
Had the game been called off before New Zealand faced five overs, it would have been declared a draw. Broad was forthright with comments that could draw sanction from the match referee.
"It would have been a good game if it had gone the full 40 overs," he said. "Both teams were in about the same position at the end of the powerplay. We could have perhaps come off earlier with the danger of the lightning. The decision-making was distinctly average from the umpires."
Heading into that pivotal fifth over, the Black Caps were three short of the D/L par at 31 for one, and lost further ground when Broad sent down successive dot balls. But with a theatrical sense of timing, McCullum swung the game in the space of four dramatic deliveries.
First, he took a step down the track and hit Broad for six following up with a thick-edge for four. Having pulled away with lightning flashing as Broad ran in, McCullum next hammered a full toss back down the ground for a maximum that took him to 16 not out in just six balls and put his side ahead of the rate.
Two more deliveries were possible before the covers were hurried on, New Zealand further extending their advantage as Kane Williamson (24no) took five runs off Chris Jordan.
England's innings began poorly as opener Alex Hales, recently rated the best T20 batsman in the world, suffered a second ball duck. A leading edge off Kyle Mills did the damage, though not without the help of a fine one-handed catch by Corey Anderson. Moeen ensured that was quickly forgotten in Mills' second over, hitting two boundaries in the "V" either side of meaty onside six.
He greeted Tim Southee's arrival with back-to-back boundaries before Lumb powered a huge six over mid-wicket as the over went for 17.
The end of the six-over powerplay saw England in good shape on 66 for one, but they stuttered when both set batsmen fell in the space of six deliveries.
Anderson first persuaded Moeen to pull straight to the waiting Mitch McClenaghan and then took a smart sliding catch when Lumb slashed to third man.
Buttler kept the momentum going with a spritely innings that included two ramp shots against Southee in the 15th over.
Exactly half of his 32 had come in fours when he was bowled by Anderson off the inside edge.
The innings might have veered badly off track had wicketkeeper Luke Ronchi held a simple catch to dismiss Ravi Bopara for seven but instead the unlucky Southee paid the price. First Bopara and then Jordan launched him over the ropes making it another expensive visit. England added 42 in the last four overs as Bopara reached 24no and Tim Bresnan a lively 17no.
As Martin Guptill and Williamson opened up for New Zealand, there was no suggestion it would be for such a brief chase.
Williamson was gifted an early boundary by Jordan's mis-field but his next two, off Bresnan, could not be stopped. Jade Dernbach struck back when he had Guptill caught from a mis-timed pull, but within moments lightning flashes arrived to disrupt proceedings.
As the groundsmen gathered on the boundary, a glance at the D/L sheets had New Zealand heading for defeat. But McCullum threw caution to the wind as he won a decisive duel with his opposite number. Despite hitting six and four from consecutive balls, the D/L scores were still tied after 4.5 overs, but McCullum's sense of occasion kicked in as he lashed a Broad full toss back down the ground for a second mighty six. The next ball from Jordan was bunted to the ropes by Williamson and, with rain imminent, England's fate was sealed.
In the earlier game, Sri Lanka beat South Africa by five runs in their opener in Chittagong.
Score: Sri Lanka 165-7 in 20 overs (K Perera 61, A Mathews 43; I Tahir 3-26, M Morkel 2-31, D Steyn 2-37) v South Africa 160-8 in 20 overs (JP Duminy 39; S Senanayake 2-22). Sri Lanka (2pts) beat South Africa (0pts) by 5 runs.