Waisake Naholo comes in on the wing and Anton Lienert-Brown at outside centre.
They replace the injured pair of Ben Smith (concussion) and Ryan Crotty (hamstring).
Ngani Laumape has also been added to the All Black's bench after the 24-year-old back impressed playing for Hurricanes in the draw with the Lions on Tuesday.
New Zealand's head coach Steve Hansen said the loss of Smith and Crotty creates an opportunity for others.
"Whilst we were happy with the win last weekend, we know that it was just a start, in what is a three-Test Series. That means the job is far from done," he added.
The Lions will be looking to bounce back after losing the first Test 30-15 in Auckland.
"We're aware the British and Irish Lions have their backs to the wall and will chuck everything at us to keep themselves alive in the series. They are a quality side who we respect immensely," added Hansen.
"In reality, last week's Test could've gone either way had they taken more of their chances."
Team: I Dagg; W Naholo, A Lienert-Brown, SB Williams, R Ioane; B Barrett, A Smith; J Moody, C Taylor, O Franks, B Retallick, S Whitelock, J Kaino, S Cane, K Read (capt).
Replacements: N Harris, W Crockett, C Faumuina, S Barrett, A Savea, TJ Perenara, A Cruden, N Laumape.
New Zealand have made two changes for the second Test against the British and Irish Lions in Wellington on Saturday.