Both replacements are uncapped at the Test level.
Latham, 21, comes in for Ryder as cover for Ross Taylor, whose wife is expected to give birth to their second child this week and may leave the team before the game begins.
"Tom's an incredibly exciting prospect and is constantly pushing for selection," National Selection Manager Bruce Edgar said in a New Zealand Cricket statement on Tuesday.
"If called upon, we're confident that he'll take the opportunity with both hands."
Neesham, 23, was not a straight replacement for Bracewell, who would not have been available due to a broken foot had he not been dropped because of the bar incident, Edgar added.
"We see Jimmy as a genuine all-rounder who can play a number of roles for us. His form with both bat and ball in the Plunket Shield this season speaks for itself," Edgar added.
"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."
New Zealand won the first Test by 40 runs at the Eden Park in Auckland on Sunday, but the victory was soured by news that Ryder and Bracewell had been out drinking on the eve of the game.
The pair were both fined for misconduct on Tuesday after NZC completed its investigation into their visit to an Auckland bar until 3 am on the eve of the first Test.
While neither had been named in the starting side, they had been expected to be ready to play if required. Team Manager Lindsay Crocker said the pair had done severe damage to their relationship with the selection panel.
'The New Zealand selectors place great emphasis on qualities such as personal responsibility, trustworthiness and dependability and will continue to do so with our encouragement,' Crocker said in a statement.
'All players in contention... need to satisfy the selectors of their commitment to prepare conscientiously for international fixtures.'
The second Test begins at Wellington's Basin Reserve on February 14.
New Zealand: Brendon McCullum (captain), Corey Anderson, Trent Boult, Peter Fulton, Tom Latham, Jimmy Neesham, Hamish Rutherford, Ish Sodhi, Tim Southee, Ross Taylor, Neil Wagner, BJ Watling, Kane Williamson
Image: Jimmy Neesham.
Photograph: Phil Walter/Getty Images
Consistency paying dividends for pacer Shami
ICC Test Rankings: India's No 2 spot at stake
Indian players suffer fall in rankings after losing Auckland Test
Stats: India have lost 10 out of the last 11 overseas Tests
1st Test: Dhoni reveals how India lost the plot