The other change comes in the centre with Gatland unable to call on the services of Andrew Bishop, Llanelli Scarlets Jonathan Davies comes in for his sixth cap.
There are also four changes on the replacements bench with No.10 Jones dropping down and Will Harries, Richie Rees and Craig Mitchell all included.
And Gatland is hoping his players can win the respect of the New Zealanders in Hamilton.
"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," said Gatland.
"But you don't get respect in this country, collectively or individually, unless you perform well on the pitch.
"This is a magnificent place to tour and we have had a wonderful welcome in Hamilton after being involved in a tough game against New Zealand last week.
"We want to leave here with our heads held high having gained the respect of this nation. We will only do that if we perform as individuals and collectively on the pitch."
Wales: Lee Byrne (Ospreys); Leigh Halfpenny (Cardiff Blues), Jonathan Davies (Scarlets), Jamie Roberts (Cardiff Blues), Tom Prydie (Ospreys); Dan Biggar (Ospreys), Mike Phillips (Ospreys); Paul James (Ospreys), Matthew Rees (Scarlets), Adam Jones (Ospreys), Bradley Davies (Cardiff Blues), Alun Wyn Jones (Ospreys), Jonathan Thomas (Ospreys), Gavin Thomas (Newport Gwent Dragons), Ryan Jones (capt, Ospreys)
Replacements: Huw Bennett (Ospreys), Craig Mitchell (Ospreys), Deiniol Jones (Cardiff Blues), Rob McCusker (Scarlets), Richie Rees (Cardiff Blues), Stephen Jones (Scarlets), Will Harries (Newport Gwent Dragons)