Pace bowler spearhead Jasprit Bumrah struck on the second ball of the day to trap Latham lbw.
New Zealand were 0-1 after two overs, as they attempt to win a Test in India for the first time in 36 years, with Devon Conway and Will Young at the crease.
New Zealand have won just two Tests in India in 36 outings, in 1969 at Nagpur and in 1988 at Mumbai.
Play began an hour late at 10:15am local time (0445 GMT) and intermittent rain is forecast throughout the day.
New Zealand dismissed India for 462 in their second innings.
India were bowled out for 46 having won the toss and opting to bat after the opening day's play was washed out without a ball being bowled. New Zealand replied with 402 in their first innings.
The second Test begins on October 24 in Pune, with the third starting on November 1 in Mumbai.
