Neesham replaced Doug Bracewell in the team while leg-spinner Ish Sodhi made way for Astle.
South Africa will need their bowlers to step up to keep their World Cup hopes alive.
Left-handed batsman Henry Nicholls is in line to make his Test debut against Australia next week with Ross Taylor ruled out of the side for the match at the Basin Reserve with a side strain.
A stat pack of India and New Zealand's ODI careers...
Matt Henry took the second five-wicket haul of his career to bowl New Zealand to a 36-run victory over Sri Lanka in the fifth one-day international and seal a 3-1 series victory at Bay Oval in Mt. Maunganui on Tuesday.
An unwell Trent Boult skipped the New Zealand cricket team's training session at the Bay Oval in Mount Maunganui on Monday, staying away from the squad as a precautionary measure. The left-arm pacer is among eight players including Ross Taylor, Colin de Grandhomme, Jeet Raval, Mitchell Santner, Tim Seifert, Tim Southee and Neil Wagner, who are attending the first half of the camp that started on Sunday.
Henry Nicholls also stroked his way to 107 - his fifth Test century - as the hosts declared at 432 for six for a 221-run first innings lead after tea on the fourth day.
Ahead of the India-New Zealand series, Rajneesh Gupta looks at the Black Caps' Test records.
The squad will then be trimmed to 15 for the ICC World Test Championship final against India at the Ageas Bowl in Southampton starting on June 18, as per ICC regulations.
New Zealand survived Ravindra Jadeja's late onslaught to stun India by 18 runs in a low-scoring thriller on Wednesday and reach the ICC World Cup final for the second time in a row.
For Kohli, a trophy-less cabinet doesn't do justice to the champion performer that he has been for a decade.
The Indian team is still searching for the right middle-order combination with the World Cup just a few months away.
New Zealand pace spearhead Trent Boult has recovered from a broken hand to be included in the 13-player squad to face India in the two-Test series, as selectors swung the axe following the dismal tour of Australia. Left-armer Boult broke his right hand in the Boxing Day Test against Australia in December but is fit for the first Test against India starting at the Basin Reserve in Wellington on Friday.
Tim Southee admitted he was disappointed not to have played in Sydney but said he has moved on.
New Zealand opening batsman Martin Guptill has been dropped for the Test series against Pakistan and the uncapped Jeet Raval is poised to make his debut.
All-rounder James Neesham has returned to the New Zealand Test squad for their three-Test tour of India.
England's sporting global ambitions have never been fully realised since Sir Alf Ramsey's team won the 1966 FIFA World Cup. Whether it is Gary Linekar or Hary Kane, the 'Cup' that they desperately want never came home during the last five and half decades.
Virat Kohli hit an unbeaten 154 to make short work of a seemingly steep target as India beat New Zealand by seven wickets in the third one-day international in Mohali to take a 2-1 lead in the five-match series on Sunday.
Pakistan will not only have to win the remaining three matches, starting with New Zealand, but also hope that the results in other matches favour them to salvage any hopes of a semi-final berth.
Uncapped batsman Henry Nicholls has been called into New Zealand's one-day squad for the start of the five-match series against Sri Lanka, while pace duo Trent Boult and Tim Southee have been rested.
New Zealand, on Monday, recalled temperamental all-rounder Corey Anderson for the five-match ODI series against India next month and he will play as a specialist batsman.
New Zealand seamer Doug Bracewell has been ruled out of this week's second Test against Australia with a shoulder injury but will not be replaced in the squad, New Zealand Cricket said on Wednesday.
India had lost to New Zealand in the semifinals of the World Cup.
Injured New Zealand pace bowlers Trent Boult and Lockie Ferguson are "tracking nicely" as the side begin their preparations for the Test series against India, according to captain Kane Williamson. Both missed the Twenty20 and One-Day International series against India but Williamson said there are hopes they could be available for the first match against the world's top ranked Test team that starts on February 21 in Wellington.
Martin Guptill has been recalled to the New Zealand Test squad for the two-match tour of England after the top-order batsman finished top scorer at the recent 50-over cricket World Cup.
Kane Williamson's assured unbeaten 70 guided New Zealand to a comfortable four-wicket win over Pakistan in the second One-Day International in Sharjah on Friday to level the series at 1-1.
New Zealand will enter the World Cup feeling optimistic of finally winning it after four and half decades of trying.
The focus will be on K L Rahul and Vijay Shankar, contenders for the number four slot, in the World Cup warm up match against New Zealand, in London, on Saturday.
India win fifth ODI to seal 4-1 series victory in New Zealand
Aston Villa returned to winning ways in stunning fashion as Ollie Watkins scored twice in a 3-0 away thumping of an abject Arsenal in drizzly north London on Sunday.
Trent Boult top the most valuable players list with Mohammed Shami hold on to second position
With the three-match T20I series ahead and also the World Cup round the corner, India will have to address this weakness to ensure that their much-vaunted batting doesn't crumble on an odd day when the condition aids swing bowling in England.
Carlos Brathwaite struck a brilliant century but West Indies still lost to New Zealand by five runs in a thrilling finish, in the World Cup match, in Manchester, on Saturday.
Langer's side secured their spot in the last four with a 64-run win over hosts England at Lord's on Tuesday and return to the famous north London ground on Saturday to face neighbours New Zealand in their penultimate round-robin tie.
Virat Kohli produced another breathtaking effort as his superbly crafted unbeaten 154 enabled India to cruise to an easy seven-wicket victory in the third ODI against New Zealand, in Mohali, on Sunday.
Thanks to Taylor's 102 and Latham's 108 (both retired out) on a flat Brabourne Stadium track, New Zealand notched up a mammoth 343 for nine in the allotted 50 overs.
A stunning spell of a fast bowling from Matt Henry ripped through the Indian top order and set New Zealand on their way to a second successive ICC World Cup final with an 18-run victory over India.
Skipper Kane Williamson's brilliant 97 and Matt Henry's maiden five-wicket haul gave New Zealand a comprehensive 68-run victory over Pakistan in the final one-dayer in Abu Dhabi on Friday. New Zealand won the series 3-2.
The West Indies are currently lying seventh in the 10-team standings with just three points in their kitty and they can't afford any further loss to stay in the mix for a semifinal spot.
