However, Morgan maintained momentum as part of his second highest T20I score. He finished on 80 not out from 46 balls and was impartial as to who he attacked.
Spin has succeeded in domestic T20 cricket at Hamilton this season, but Mitchell Santner, Sodhi and Kane Williamson struggled to use that to their advantage against England's juggernaut.
Santner was brought back into the New Zealand side after Ben Wheeler's expensive outing at Eden Park against Australia.
His bandaged right knee had recovered sufficiently to play, but England offered no mercy, taking him for 11 from the second over of the game.
When the left-arm orthodox spinner returned in the 11th, Morgan continued the assault with 19 runs from his bat. Two wides worsened the punishment. He didn't bowl again.
Before the match, Santner had 28 wickets in 25 T20 internationals at an average of 19.96, economy rate of 6.88 and strike rate of 17.
That was enhanced in three matches against England, where the 26-year-old has five wickets at an average of 17, economy rate of 7.61 and strike rate of 13.
That included Tuesday's 12-run win at Westpac Stadium, in which he bowled two overs in the powerplay and conceded 12 runs - and two leg byes - to tie down England.
Sodhi offered more control. His first and fourth overs cost three runs apiece and included Buttler's wicket. They bookended concessions of 11 and 14 runs.
Captain Williamson brought himself on in the seventh over - after the powerplay - to take his off breaks away from left-handers Malan and Morgan. They were on to his ruse and picked him off for 16 runs - taking eight runs apiece including two sixes.
Southee provided the highlight of the bowling performance with a 'Richie Benaud special' of two for 22. He found a controlled length by conceding two runs - including a wide - and removing Hales with a slower ball in the third over. He also removed David Willey to dam England's flow at the death.
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