Patrick Tuipulotu will take Barrett's place in the second row in Wellington on Saturday, while Caleb Clarke comes in on the left wing in place of Sevu Reece, who suffered a grade-one head knock in the first minute of the first Test.
Rieko Ioane moves from the left to the right wing, and uncapped Highlanders centre Timoci Tavatavanawai joins the reserve bench.
Robertson was expected to make more changes after a dire first Test performance in which the All Blacks scraped home 31-27 against a French team stripped of most of their Six Nations stars.
Ioane is lucky to retain his place in the starting line-up after a poor first Test performance. His failure to secure the kickoff at the start of the second half led directly to a France try.
Robertson has also retained Beauden Barrett at flyhalf, though Barrett's tactical kicking game in the first Test was flawed and New Zealand were unable to win recoverable kicks.
"Test series are a unique and exciting opportunity," Robertson said.
"Both teams now have a better idea of what they're going to get on Saturday night and both will lift for this next occasion.
"We know where we need to improve."
Improvement is needed across the board unless the All Blacks are to produce another of the rudderless performances that have become typical during Robertson's tenure.
New Zealand were beaten by France in the aerial contest in the first Test in Dunedin. The selection of Clarke may help with that.
There was also a lack of physicality at the breakdown, which the All Blacks will have to find on Saturday to prevent another close finish.
Robertson has retained lock Fabian Holland and back-rower Christian Lio-Willie, who made solid debuts last weekend.
First test debutants Ollie Norris and Du'Plessis Kirifi have also been retained among a 5-3 split on the bench.
NEW ZEALAND: Will Jordan, Rieko Ioane, Billy Proctor, Jordie Barrett, Caleb Clarke, Beauden Barrett, Cam Roigard; Christian Lio-Willie, Ardie Savea (captain), Tupou Vaa'i, Fabian Holland, Patrick Tuipulotu, Fletcher Newell, Codie Taylor, Ethan de Groot
Reserves: Samisoni Taukei'aho, Ollie Norris, Pasilio Tosi, Samipeni Finau, Du'Plessis Kirifi, Cortez Ratima, Timoci Tavatavanawai, Damian McKenzie
