The 90-times capped Jones is included among the replacements, while Scarlets centre Jonathan Davies is the other change to the starting XV in Dunedin as he replaces the injured Andrew Bishop alongside Jamie Roberts at centre.
There are a further four changes on the bench with Dragons wing Will Harries and Blues scrum half Richie Rees joining Jones in providing cover for the backs and Ospreys prop Craig Mitchell comes in for the Blues John Yapp, who turned an ankle in training this week.
Ospreys hooker Huw Bennett, Blues lock Deiniol Jones and Scarlets flanker Rob McCusker are all retained as replacements with Scarlets' young scrum half Tavis Knoyle missing out this week.
"This is a magnificent place to tour and we have received a wonderful welcome in Hamilton after being involved in a tough game against New Zealand last week," said Gatland.
"There is a lot of mutual respect amongst the players and the people of New Zealand and Wales and we are two nations who love our rugby, but you don't get respect in this country, collectively or individually, unless you perform on the pitch here.
"Kiwis talk fondly about the Welshmen involved in the 1971 Lions tour because they won the series, they talk glowingly about players like Ryan Jones who made an impact on the pitch on the 2005 Lions tour.
"We want to leave here with our heads held high after Saturday and with the respect of the New Zealand nation and we will only do that if we perform as individuals and collectively on the pitch.
"This team has an opportunity to create a reputation in this country that will last into the Rugby World Cup next year and beyond and we need to take that opportunity."
WALES: Lee Byrne; Leigh Halfpenny, Jonathan Davies, Jamie Roberts, Tom Prydie; Dan Biggar, Mike Phillips; Paul James, Matthew Rees, Adam Jones, Bradley Davies, Alun Wyn Jones, Jonathan Thomas, Gavin Thomas, Ryan Jones (capt)
Replacements: Huw Bennett, Craig Mitchell, Deiniol Jones, Rob McCusker, Richard Rees, Stephen Jones, Will Harries
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