Doug Bracewell stays in the squad despite not getting a run in the Sri Lankan ODI series, while Todd Astle will also be considered for the final two games of the series if he, too, can prove his fitness in the Super Smash.
Black Caps coach Gary Stead said his squad is a result of juggling multiple objectives – preparing for the upcoming World Cup, and aiming for a series win against a high-quality Indian outfit.
"Our two main priorities have been to select and prepare a squad capable of winning what is shaping as a massive series against India, and gathering as much information as possible ahead of the World Cup," said Stead.
"Tom and Colin are experienced players in this format and will offer quality in their respective roles, and Mitch and Doug showed us what they are capable of during the T20 on Friday night."
Stead is hopeful that Neesham and Astle will join the squad for games four and five, if they come through the Super Smash unscathed.
"We were impressed by Jimmy against Sri Lanka, and are keen to see more of Todd – who has a different skillset and performed well for us last year.
"It's just important that, after their respective injuries, we can see them playing again and be confident of bringing them back at this level."
The ODI series kicks off at McLean Park in Napier next Wednesday.
Black Caps squad
Kane Williamson (c), Trent Boult, Doug Bracewell, Colin de Grandhomme, Lockie Ferguson, Martin Guptill, Matt Henry, Tom Latham, Colin Munro, Henry Nicholls, Mitchell Santner, Ish Sodhi, Tim Southee, Ross Taylor.