A wave of criticism swept over Foster after the All Blacks scraped a 16-16 draw in the first test against a resurgent Wallabies last Sunday in Wellington, a true baptism of fire for the former assistant to Steve Hansen.
Vaa'i joins Patrick Tuipulotu in the second row in pace of veteran Sam Whitelock, who has a head injury. The bench also features Alex Hodgman, who could make his Test debut for the All Blacks.
Gardner, who was a touch judge in the first Test, swaps roles with Williams for the second Test and Rennie said the Australian camp had gone through the "right channels" in their correspondence with referees, via World Rugby referees boss Paddy O'Brien.
Among other things, Rieko Ioane was sacked from the start, with Anton Lienert-Brown named in the centers and Caleb Clarke replacing the injured winger George Bridge.
In other changes, Dane Coles will take over at hooker from Codie Taylor and Anton Lienert-Brown will start at center, displacing Rieko Ioane.
The All Blacks replacements also include the 36-Test Scott Barrett, who has been sidelined by a foot injury for the past three months.
Barrett missed the first game due to injury and was replaced by Damian McKenzie in the starting XV but the latter now drops to the bench. We need to be smarter with our ball and more focussed defensively.
But whenever Australia has started a Bledisloe series well in recent years they have generally been thrashed the following week, and Foster warned they can again expect a vast improvement from the All Blacks.
Hanigan has not played a Test since 2018 but Rennie said the 25-year-old deserved an worldwide recall based on his training performances.
On the selection of Vaa'i and Hodgman, Foster said: "It's a great opportunity for Tupou".
"He's done a lot of work around the All Blacks and the opposition stuff leading into last weekend's game".
"Ned has been really impressive and has trained really well in the four weeks we have been together", said Rennie. "He's mobile and he's been making big strides in his scrummaging, so it's a big opportunity for him in his first test".
The third and fourth Tests will be played in Australia on October 31 and November 7 as part of the Rugby Championship, which also involves Argentina.
The All Blacks' performance mirrored the World Cup semifinal in Yokohama previous year when they were thoroughly outplayed by a harder and tougher England pack.
New Zealand hasn't lost to any nation on Eden Park since 1994, and hasn't lost to Australia at the venue since 1986, before any player on either side was born.