The 182-operate partnership in between Malan and Morgan was also England's greatest in T20s.
Dawid Malan broke an England history with a fantastic century in opposition to New Zealand in the fourth 2020 worldwide in Napier on Friday.
Malan became only the second Englishman to hit a century in a Twenty20 worldwide when he smacked his sixth six, reaching the mark quicker than Alex Hales with his 60-ball hundred against Sri Lanka during the 2014 World Cup.
Malan finished 103 not out. He averaged just 23.77 from five matches with just one half-century.
Malan said Morgan launched the England attack "and I sort of jumped in his slipstream".
"I got to about 80 and I thought these boundaries are so small I may as well have a crack".
Their assault neutralised a shaky start with Jonny Bairstow (8) falling in the fourth over. And, having reached his half-century from 31 balls, he accelerated sharply to record his century just 17 deliveries later.
21 - Balls taken by Morgan to complete his fifty, the fastest by an England batsman in the format.
In fairness, the New Zealanders could have bowled excellently and it may not have made a difference, such was the power and precision with which Malan and Morgan were striking.
The pair smacked 76 runs from the 10th to the 14th overs, achieving an nearly unstoppable momentum.
They then helped England add 85 in the last five overs with only left-arm spinner Mitchell Santner (2-32) emerging with any credit.
There wasn't much else they could do but hit and hope, and Southee at least ensured his side would avoid a record rout by smashing a rapid 39 from 15 balls.
Bairstow will remain with the squad after the end of the T20I series which concludes on Sunday (November 10) at Eden park in Auckland and provide cover for England's two-day warm-up match against a New Zealand Cricket XI and the three-day game against New Zealand "A", both to be played at Cobham Oval, Whangarei.