Anton Lienert-Brown and Jack Goodhue will start in the centres, while Umaga-Jensen could join reserve prop Alex Hodgman in making his first appearance in the black jersey if he is required to sit on the bench.
Damian McKenzie, a late starter in the drawn first Test when Barrett was ruled out on the eve of the match, will take his place on the bench.
The All Blacks play the Wallabies at 3pm Sunday at Eden Park.
"I can't speak from a Test perspective but I've coached a lot of Chiefs teams against the Blues at Eden Park and we've never lost one", Rennie said.
Bridge is out for up to six months after suffering a chest injury in training, while Sam Whitelock is also out of tomorrow's match because of due to headaches.
Anton Lienert-Brown replaces Ioane, as coach Ian Foster makes four changes to his starting line-up from the 16-16 draw in Wellington.
Caleb Clarke, who made his debut off the bench last week, has been fast-tracked into the run-on XV to replace the injured George Bridge at left wing.
"It was our first Test together last weekend and while there were some aspects of our game that we were pretty excited about, especially around our set piece, we didn't get the performance that we wanted, so there has been plenty for us to work on".
"We need to be smarter with our ball and more focussed defensively".
"It's the last Test at home for us so there will also be massive excitement amongst our fans".
"Definitely there's the hype of Eden Park - The Fortress - but the mindset for us is it's just another field, just another game, just another place we're going to play", Paenga-Amosa said.
On the selection of Vaa'i and Hodgman, Foster said: "It's a great opportunity for Tupou".
"Alex has been impressive in the training weeks".
The All Blacks and Australia will be playing their 168th test against each other.
Centre Rieko Ioane has been dropped from the starting line-up by New Zealand for Sunday's second Bledisloe Cup Test against Australia, live on Sky Sports.
A win would boost their chances of reclaiming the Bledisloe Cup, which the All Blacks have held since 2003.