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England, having lost to New Zealand by 12 runs last week, need to win the match and finish with a better overall run-rate than the Kiwis if they are to make Wednesday's final in Auckland against Australia.
Morgan, who missed the last two England matches because of a groin strain, had six sixes and four fours in his crucial innings.
He went to the middle in the fourth over when England were two for 24 and featured in a 93-run, nine over stand with Dawid Malan.
Malan was eventually dismissed for 53, his fourth half-century in five international Twenty20 innings.
With a place in the finals riding on the game, New Zealand skipper Kane Williamson did not want to let the England batsmen settle when he won the toss and opted to bowl.