The Black Caps, invited to bat first at the Feroz Shah Kotla stadium in New Delhi, rode on a 85-run second-wicket partnership between Latham, who retired after scoring 55, and Williamson to put up a challenging score.
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The Aditya Tare-led Mumbai were 29 for one at stumps, trailing the visitors by 295 runs in the first innings.
New Zealand's pace spearhead Trent Boult claimed the only wicket of opener Jay Bista, who was caught behind for nought. Kaustubh Pawar on five and Armaan Jaffer on 24 were at the crease.
However the day belonged to the New Zealand batsmen, who scored at more than four runs an over against a Mumbai attack that used nine of their bowling options.
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Ross Taylor, who made 41, and Mitchell Santner, whose 45 came off 59 deliveries, also made significant contributions.
The two sides have 15 members each, with only 11 allowed to bat and field in the only warm-up tie before the three-match Test series starting September 22 in Kanpur.
Brief Scores:
New Zealenders 324/7 dec (Tom Latham 55, Kane Williamson 50; Balwinder Sandhu 2-21)
Mumbai 29/1 (Armaan Jaffer 24 not out, Kaustubh Pawar 5 not out; Trent Boult 1-5)
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