Neesham replaced Doug Bracewell in the team while leg-spinner Ish Sodhi made way for Astle.
Taylor, who missed the third game in Wellington with a quadriceps injury, was limping badly after he appeared to suffer a similar strain but still combined with Tom Latham (71) for 187 runs as New Zealand scored 339 for five in 49.3 overs to chase down England's 335 for nine.
Images from Day 4 of the third Test between Australia and New Zealand in Sydney on Monday.
New Zealand ripped through Australia's batting line-up on a lethal wicket to leave the hosts foundering on 81 for seven in their first innings at lunch on the second day of the second Test on Saturday.
Delhi Daredevils all-rounder Irfan Pathan has called on the middle-order batsmen of his side to fill in the gap left by Kevin Pietersen, and also hoped that struggling Kiwi batsman Ross Taylor would soon regain his lost touch.
His form has been a bit of concern but New Zealand captain Ross Taylor is confident that Delhi Daredevils' untested middle-order will "stand up" and be counted when required in the Indian Premier League.
New Zealand's hopes of recording their first victory over Australia in almost 20 years have been boosted after a raft of injuries forced their trans-Tasman neighbours to pick a rookie trio of pace bowlers and an opener untried in Test cricket.
Images from Day 3 in the second Test between India and New Zealand, in Mumbai on Sunday.
New Zealand pacer Tim Southee said their World Test Championship triumph will take at least a couple of weeks to sink in.
New Zealand finished the fourth day of the final Test 274 runs behind South Africa on Monday and lost Ross Taylor to a broken arm after the skipper was struck by a Morne Morkel bouncer.
New Zealand's nine-wicket loss to South Africa in the second Test was a closer match than the result suggests and the hosts' captain Ross Taylor believes his team is not far away from being competitive in the third Test in Wellington.
The play stopped for a brief moment at Bay Oval in Mount Maunganui, when a streaker came running to the pitch.
Captain Ross Taylor and Brendon McCullum kept New Zealand's slim hopes of scoring 401 runs to beat South Africa in the first Test alive after they helped the hosts reach 137 for two at the close of the fourth day's play at University Oval in Dunedin on Saturday.
Images from Day 5 of the first Test between India and New Zealand, at Green Park in Kanpur, on Monday.
New Zealand vice-captain Tom Latham says losing the first day to rain will not change their approach to team selection.
New Zealand captain Ross Taylor led from the front with an unbeaten 119 as New Zealand ended the first day of the second Test against Sri Lanka on 223 for two wickets on Sunday.
New Zealand's captain Ross Taylor's 111 not out has put the hosts in a commanding position against Zimbabwe. New Zealand are five for 331 on the first day of the one-off Test against Zimbabwe in Napier on Thursday.
Ben Wheeler will replace Jacob Oram in the Central Stags squad for the 2010 Airtel Champions League Twenty20, in South Africa from September 10-26. The tournament's Technical Committee on Friday allowed the change after scans confirmed the injury-plagued New Zealand all-rounder will require surgery on his injured knee.
New Zealanders will be proud of the fight their cricket team showed to stage a remarkable turnaround and claim their first Test victory on Australian soil in 26 years, Black Caps skipper Ross Taylor said on Monday.
New Zealand will play their first home Test against Zimbabwe in 11 years, as well as a three-match series against South Africa, in the next southern hemisphere summer, New Zealand Cricket announced on Friday.
The hosts ended the day on 144-4 and Henry Nicholls (26) and BJ Watling (six) will resume in Mt. Maunganui on Saturday to try and eat into their 209-run deficit after England were dismissed for 353 after lunch on Friday.
Martin Guptill hit his second Test century to put New Zealand in firm control of their one-off Test against Zimbabwe at Queens Sports Club on Tuesday.
Malcolm Waller hit a single off the fifth ball of the last over to take Zimbabwe to a dramatic one-wicket win in the third and final One-day International against New Zealand at Queens Sports Club.
New Zealand cricket will get a million dollars if Central Districts' three Indian Premier League players are wanted by their franchises for Champions League in South Africa.
Neesham, a batting all-rounder, rocked the Afghanistan innings by his incisive bowling and in the process returned with his career-best figures of 5/31 from his 10 overs. His earlier best was 4/42.
Kane Williamson's sentiment was also echoed by one of his senior teammates Ross Taylor, who was also critical of the points system.
Birthday boy Ross Taylor rode his luck to good effect and scored a spectacular 131 not out as New Zealand registered a comprehensive 110-run win over Pakistan in the World Cup Group A encounter in Pallekele (Kandy) on Tuesday.
New Zealand sought to put behind their dismal record of losing 14 of their last 17 ODIs coming into the World Cup, saying that they are still a strong side capable of winning the coveted trophy.
With all-rounder Cameron White choosing Royal Challengers Bangalore, the Victoria Bushrangers will now be captained by David Hussey in the Champions League T20 cricket tournament starting September 10 in South Africa.
Half-centuries from Ross Taylor and Scott Styris guided New Zealand to a thumping 200 run-victory over India in the opening match of the one-day tri-series in Dambulla on Tuesday.
India recorded their biggest defeat to New Zealand in terms of runs, surpassing the 108-run loss at Dunedin on March 1, 1990.
New Zealand batsman Ross Taylor is aware that another cheap dismissal in the second Test against Pakistan could give rise to questions about his eye condition and whether it has affected his performance.
Latham, De Grandhomme lead NZ to series sweep of India
Royal Challengers Bangalore (RCB) has indicated they will exercise their right to select Ross Taylor in their 15-man Champions League squad, which would prove to be an unexpected windfall for New Zealand Cricket.
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.
Kane Williamson's career has many more years left to run but the New Zealand captain reached the first of many milestones predicted of him since his breakthrough as a teenager with a routine shot in the first Test against England on Friday.
New Zealand's stand-in skipper Ross Taylor was disappointed after the Black Caps crashed to their seventh consecutive One-day International defeats in Guwahati, but hoped to get their act together before the forthcoming World Cup in February.
Ross Taylor smashed a quickfire unbeaten 47 as Rajasthan Royals thumped Pune Warriors by six wickets in a thrilling encounter to jump to the top of the table in Indian Premier League in Jaipur on Sunday.
Hard-hitting New Zealander Ross Taylor on Saturday admitted Rajasthan Royals has not been up to the mark but said they would look to exploit the home conditions to bring their IPL campaign back on track on Sunday.