Neesham and Latham were added to the squad after selectors decided to drop Jesse Ryder and Doug Bracewell following their late-night drinking spree before the first Test in Auckland.
While Latham is a replacement for Ryder, who was a cover for Ross Taylor, Neesham is likely to play a "number of roles" for New Zealand which named an otherwise unchanged squad from the victorious first Test at Eden Park.
New Zealand Cricket General Manager National Selection Bruce Edgar said that Neesham is not necessarily a straight replacement for Bracewell.
"We've been able to keep a settled side recently and strung together some successful results along the way. We hope to keep that going, but are well aware India will come back at us hard."
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Taylor, who is awaiting the birth of his second child, might make way for 21-year-old Latham in the playing XI if the veteran's baby doesn't not "arrive by the start of the Test".
It is a good time for New Zealand cricket as their unchanged squad enjoyed a 2-0 series win over the West Indies and scored a 40-run victory over India in a thrilling opening Test in the last three successive Tests.
New Zealand Squad: Brendon McCullum (C), Peter Fulton, Hamish Rutherford, Kane Williamson, Ross Taylor, Corey Anderson, BJ Watling (WC), Tim Southee, Ish Sodhi, Neil Wagner, Trent Boult, Jimmy Neesham, Tom Latham.