After Tim Southee bowled the Black Caps back into contention with a five-for, Latham and Young produced the first century partnership by a visiting team on Indian soil in five years.
At stumps, Latham was 50 not out and Young 75 not out. Play ended due to bad light with three overs remaining.
They trail by 216 runs after bowling out India for 345 three overs after lunch. Shreyas Iyer led with 105, a century on debut.
Southee took 5-69 and fellow fast bowler Kyle Jamieson 3-91. Spinner Ajaz Patel made short work of the tail to finish with 2-90.
Thereafter, New Zealand didn’t give a single whiff to the India bowlers.
Latham and Young added 72 runs before tea and completely stumped the India attack with their defiance.
Their 50-run stand came up in 125 balls.
After tea, they continued to grind against the spinners, who were at fault for bowling too flat.
Ravichandran Ashwin (0-38), Ravindra Jadeja (0-28) and Axar Patel (0-26) bowled 41 overs of the 57 faced by the openers.
Latham was forced to use reviews and overturned three dismissal decisions against him.
He went on to score his 21st test half-century off 157 balls, including four fours.
Young played more attacking cricket as he finished the day with 12 boundaries. He, too, reached his second half-century off 88 deliveries.
The last openers to combine for a century in India were England’s Alastair Cook and Keaton Jennings in 2016 at Chennai.
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