Malan struck nine fours and six sixes during his unbeaten knock.
Malan's century off 48 balls was the fastest ever by an England player as he toyed with New Zealand's bowling attack on Friday.
The pair hold the highest third-wicket partnership by any side in a T20 global.
Malan scored 103 not out and stitched a 182-run partnership with skipper Morgan (91) to help England post their highest T20I total of 241/3, surpassing their previous-best of 230/8 against South Africa in the 2016 World T20.
Joining forces in the eighth over with England at 58-2, the pair added a mammoth 182 from just 76 balls to launch the visitors to 241-3 - England's highest Twenty20 total - with Malan (103 not out) producing their highest individual innings.
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Malan became just the second Englishman to make a century in the format, but was considerably more rapidly than Alex Hales' 60-ball work from Sri Lanka in 2014.
Guptill hit a boundary in the next over, delivered by Sam Curran, but his innings came to a sudden halt on the next ball.
However Malan provided the inexorable thrust, posting a second half century from 17 deliveries and reaching a century which included nine fours and six sixes.
Morgan, at the other end, put up a six-hitting display of his own, clobbering seven of them as he threatened to eclipse Malan's hundred. Ish Sodhi's figures - he conceded 49 from three overs, with his final one costing 28 - were particularly ugly, though Blair Tickner recovered relatively well after his first two overs cost 32.
The England captain, twice caught off waist-high full-tosses which were subsequently adjudged no-balls, eventually holed out after his 41-ball blitz. Morgan walked out to join Malan and the left-handers lit up McLean Park. He bettered Jos Buttler's 22-ball effort against Australia at Edgbaston past year.