Julian Savea returns on the left wing after being dropped for the second Test last weekend in Dunedin.
Dixon, 26, comes in for Jerome Kaino on the side of the scrum, with Squire coming into the matchday 23 for Ardie Savea as loose forward cover. Prop Charlie Faumuina replaces Owen Franks in the number three jersey, with 24-year-old Tu’ungafasi coming into the 23.
In the backs, Beauden Barrett is at fly-half, replacing the injured Aaron Cruden, with Lima Sopoaga the 10 reserve; George Moala will start at centre in his second Test replacing the injured Malakai Fekitoa; and Savea is back in the 11 jersey, with Waisake Naholo moving to the bench as outside back cover.
In other changes to the matchday 23, Codie Taylor has been named at replacement hooker, Luke Romano comes in as lock cover and Tawera Kerr-Barlow is the replacement half-back.
It will be a special night also for lock Brodie Retallick and Aaron Smith, who will play their 50th Tests for the All Blacks. The pair made their Test debuts in the same Test, against Ireland in June 2012.
Hansen said, in selecting the side, the selectors had to take into consideration the need to find out more about the squad.
“With the Series won, it came down to risk and reward and we felt the rewards of seeing these new players in the Test arena, after watching them for three weeks on the training pitch, outweighed any risks,” he said.
“It’ll be exciting to see these new players making their mark for the first time in the black jersey.
“That said, we’re expecting another brutal Test match, with the expectation that Wales will again chuck the kitchen sink at us. We’ve seen over the last two Tests that they’re a very good side who play physical, combative and innovative rugby. Our own expectations are as high as ever and we’ll be looking for continued improvement right across our game.
“We have a further two players playing their 50th Test this weekend. On behalf of the team, we would like to congratulate Aaron and Brodie on reaching this special milestone and they can be rightly proud of everything they have achieved so far in the black jersey.”
Commenting on the Test match atmosphere in Dunedin, Hansen added: “Playing here in Dunedin is always something special because of the enclosed stadium. There’s no need to worry about the weather and it’s always a hard and fast pitch, while the proximity of the crowd also creates an awesome atmosphere.”
New Zealand: 15 Israel Dagg, 14 Ben Smith, 13 George Moala, 12 Ryan Crotty, 11 Julian Savea, 10 Beauden Barrett, 9 Aaron Smith, 8 Kieran Read (c), 7 Sam Cane, 6 Elliot Dixon, 5 Sam Whitelock, 4 Brodie Retallick, 3 Charlie Faumuina, 2 Dane Coles, 1 Joe Moody
Replacements: 16 Codie Taylor, 17 Wyatt Crockett, 18 Ofa Tu’ungafasi, 19 Luke Romano, 20 Liam Squire, 21 Tawera Kerr-Barlow, 22 Lima Sopoaga, 23 Waisake Naholo