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Hazlewood's inexorable line and length, just on off stump and ducking away, was too much for the New Zealand top order.
New Zealand consolidated their position at the top of the World Test Championship standings with 36 points and a winning percentage of 75.
New Zealand dashed India's hopes in the semifinals of the 2019 edition and Williamson said he was not concerned that his side were still considered underdogs.
New Zealand occupy the last semifinal slot available but only by virtue of having a better net run rate than Pakistan and Afghanistan, with all three teams tied on eight points after eight games.
Both Pakistan and New Zealand have eight from as many games with one match remaining.
Tom Blundell will travel to India as cover, but Williamson will remain with the team with the hope of being available for the back end of group play next month.
Williamson missed wins over defending champions England and the Netherlands to work on his fielding and running between the wickets.
Tom Latham is set to lead New Zealand in what would be a rematch of the 2019 final.
Boult, Williamson, Neesham, fast bowler Tim Southee and wicketkeeper-batsman Tom Latham form a strong core of World Cup veterans but the squad also includes six players looking to make their debut at the 50-over tournament.
Back near 100 per cent in terms of his batting movement in the nets at training, Williamson said the next three weeks would decide whether he would be fit for New Zealand's opener against England on October 5.