Canterbury full-back Leon MacDonald was due to replace Carter at fly-half but has failed to overcome a groin strain suffered in training earlier in the week.
North Harbour's Luke McAlister, who was only drafted into the squad on Monday because of injuries to Carter (shoulder) and Mauger (hamstring), will start at pivot with another late call-up, Otago's Nick Evans, coming on to the bench.
Wellington's Conrad Smith comes in for Mauger in midfield.
Prop Carl Hayman and hooker Anton Oliver were not considered due to injury.
On the bench, lock James Ryan replaces Jono Gibbes.
As a result of the changes the All Blacks have been forced to reshuffle their backline with captain Tana Umaga moving to inside centre to accommodate his fellow Hurricane Smith at outside centre.
Henry is determined the All Blacks will go for the jugular on Saturday when they aim to complete only the third clean sweep in Lions Test history.
"We are taking the Test very seriously and we have put our best team out on the field," explained a chirpy Henry.
"If Daniel [Carter] had been fit he would have obviously been in the side. But we are making some progress and we are pleased with the progress we are making. We think we can still move further up the graph.
"So we had a policy in team selection to pick our best team to play in this Test match.
"I think the challenge is to get the guys up physically. They are very sore as they have played two huge Tests within a couple of weeks.
"They had a very physical encounter last week. We have to give them sufficient rest so they can play fairly well on Saturday."
The Lions may be still reeling from last weekend's record second Test 48-18 defeat at Westpac Stadium but Henry remains adamant there is room for improvement among All Blacks ranks.
"We've got things to work on," he said. "We didn't start the game very well, our heads weren't right really. We wanted to play well, we were physically there but weren't quite there upstairs and we need to learn from that situation."
New Zealand team for third Test in Auckland: Mils Muliaina; Sitiveni Sivivatu, Conrad Smith, Tana Umaga (capt), Rico Gear; Byron Kelleher, Luke McAlister; Tony Woodcock, Keven Mealamu, Greg Somerville, Chris Jack, Ali Williams, Jerry Collins, Richie McCaw, Rodney So'oialo.
Reserves: Derren Witcombe, Campbell Johnstone, James Ryan, Sione Lauaki, Justin Marshall, Nick Evans, Doug Howlett.