In a six-hitting spectacular at Eden Park on Saturday, the tourists finished streets ahead with 15 of the 23 struck - many over the uniquely short straight boundaries at the venue.
After Eoin Morgan and Luke Wright had powered England to 214 for seven, 12 runs more than the former World Twenty20 champions have ever previously made in the shortest format, Broad's career-best four for 24 helped complete the job.
New Zealand's 174 for nine under lights left them losers by 40 runs and 1-0 down with two matches still to play in the three-match series in Hamilton and Wellington.
Morgan's 46 was England's top score, but their six-hitters just kept coming - and then Wright, Steven Finn (three for 39) and Broad provided the wickets which meant the hosts' run chase was never quite competitive.
The England captain reflected afterwards on an impressive collective performance which left him wanting more of the same.
"It was a really good experience to be out there today - a record batting score for us, and the energy out there in the field was fantastic," Broad said. "It was really calm, but a lot of buzz out there - and that's what you're looking for. It was pretty much the complete performance from us today.
"The power we have is hugely exciting. Our challenge now is to make it as good as it was today at Hamilton [on Tuesday]."
The strange dimensions of the playing surface for this first match lend themselves to an extreme version of cricket.
"You're not going to see smaller straight boundaries than that - fielding at mid-off was pretty much long-off," Broad said.
"But some of the striking would be sixes anywhere in the world."
Even with England's best-ever total on the board, Broad knew he could not take New Zealand's destructive batting line-up lightly - and he was relieved to see Morgan take a cool catch under a mis-hit skier to see off home captain Brendon McCullum early.
"We were very aware that wickets were going to be crucial for us, and that's why Morgan's catch was absolutely fantastic to get rid of such a key man."
McCullum rued his own team's poor catching - five chances went down in all - and gave due credit to England.
"They put us under pressure right from the get-go, and we were never able to claw it back," he said.
"No one means to drop catches. But five drops in a Twenty20 game is never going to help your cause. It's an area we normally pride ourselves on.
"Tonight we were off the pace, with our bowling and batting as well."
England win first Twenty20 by 40 runs
Second Twenty20 match, at Hamilton
Third Twenty20 match, at Wellington
Bangladesh pick Jurgensen to lead them
Australian Shane Jurgensen has been promoted from bowling coach to head coach of Bangladesh on a one-year deal.
Jurgensen guided Bangladesh to a 3-2 one-day international series win against West Indies at home in December when acting as interim coach after Englishman Richard Pybus refused to continue after a contract dispute.
“We had several candidates for the position of head coach. But there was no one better than Jurgensen,” said Jalal Younus, the chairman of the Bangladesh Cricket Board media committee.
“So we decided to appoint him as head coach up to December 2013.”
Jurgensen’s first assignment will be a visit to Sri Lanka for a two-Test and three one-day international series, starting in March.
Younus said former Pakistan spinner Saqlain Mushtaq could also return to the coaching staff if a deal can be agreed.
“Saqlain told us he will be available for maximum 100 days in a year. We are now trying to sort out when actually we need his services. If everything goes according to plan he also can join us,” Younus said.
Mushtaq worked as spin bowling coach for Bangladesh from August to December last year.
Meanwhile, Australia captain Michael Clarke will be rested from Sunday’s final one-day match due to continuing right hamstring soreness which flared up after Friday’s five-wicket win over the West Indies at the Sydney Cricket Ground.
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