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Former white-ball captain Morgan, who bowed out of the international game last June, led England to 50-over World Cup glory on home soil and the top of the one-day and Twenty20 rankings.
On a pitch where England's star-studded batting lineup struggled to clear the ropes, Neesham belted three sixes in his audacious late-order assault.
Daryl Mitchell smashed an unbeaten 72 as New Zealand chased down their 167-run target with an over to spare.
The defending champions, Windies have left out Roston Chase.
The England white-ball captain expects to play in next year's Twenty20 World Cup.
Kolkata failed to capitalise on a great start in reply to Chennai's 192/3 as the MD Dhoni-led side powered to a fourth IPL title in Dubai.
During last week's IPL match between Delhi Capitals and Kolkata Knight Riders, which is captained by Morgan, Ashwin tried to take a run after a throw ricocheted off his batting partner Rishabh Pant's body.
From a comfortable position of 96/1, KKR dragged themselves into a difficult situation in the end. They will play CSK in the final on Friday.
Delhi skipper Pant and Ashwin had picked up a second run when the ball thrown by the fielder ricocheted off the batter and that seemed to have irked the KKR outfit.
Steve Smith and Rishabh Pant top-scored with 39.
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