Basham, 27, has been recalled for the Nations Championship clash against the All Blacks after Aaron Wainwright, who featured in the position during last Saturday's 28-21 win over Japan in Wales' November Nations Championship opener, was ruled out with a minor calf injury.
Another back-row change sees James Botham, the grandson of England cricket great Ian Botham, start at blindside flanker, with Adam Beard in the second row and Gabriel Hamer-Webb on the left wing.
The All Blacks have dominated this fixture, posting 34 successive wins over Wales since their last loss back in 1953.
"We're excited for the opportunity we have against New Zealand," said Wales coach Steve Tandy.
"It was good to get the win last Saturday, but some elements of our execution weren't where we wanted.
"We have to go up another level this weekend and be more ruthless. We have one of the best teams in the world coming. We want to be better and put in an 80-minute performance."
Turning to Cardiff loose forward Basham, he added: "I'm delighted that Taine gets an opportunity this weekend. It's been a while since his last appearance for Wales, but he didn't give up and has put in a lot of dedication and hard work to get back."
Wales team:
Starters: 15-Blair Murray; 14-Louis Rees-Zammit, 13-Eddie James, 12-Max Llewellyn, 11-Gabriel Hamer-Webb; 10-Sam Costelow, 9-Tomos Williams; 8-Taine Basham, 7-Jac Morgan, 6-James Botham; 5-Adam Beard, 4-Dafydd Jenkins; 3-Archie Griffin, 2-Dewi Lake (capt), 1-Nicky Smith
Replacements: 16-Ryan Elias, 17-Gareth Thomas, 18-Dillon Lewis, 19-Ben Carter, 20-Taine Plumtree, 21-Reuben Morgan-Williams, 22-Dan Edwards, 23-Louie Hennessey
New Zealand team:
Starters: 15-Beauden Barrett, 14-Fehi Fineanganofo, 13-Quinn Tupaea, 12-Anton Lienert-Brown, 11-Josh Moorby, 10-Richie Mo’unga, 9-Cortez Ratima, 8-Wallace Sititi, 7-Peter Lakai, 6-Anton Segner, 5-Josh Lord, 4-Scott Barrett, 3-Fletcher Newell, 2-Asafo Aumua, 1-George Bower
Replacements: 16-George Bell, 17-Xavier Numia, 18-Pasilio Tosi, 19-Jamie Hannah, 20-Ethan Blackadder, 21-Leicester Fainga’anuku, 22-Kyle Preston, 23-Rieko Ioane
Nations Championship 2026
The inaugural Nations Championship will see six northern hemisphere and six southern hemisphere nations battle it out across six rounds in the July and November international windows before assembling in Twickenham for one unforgettable finals weekend on November 27-29.
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