Chasing 176 in 16 overs, New Zealand were 63/4 at one point before debutant Conway and Neesham resurrected the innings with a rapid partnership of 77 in 35 balls.
Conway showed excellent composure amidst the quick wickets lost, while Neesham started off with a bang, hitting two fours off his first two balls. He went on to hammer 23 runs in a Kesrick Williams over to bring the required run-rate down.