Will Genia has been elevated to the captaincy, with Michael Hooper promoted to the run-on side.
Cooper has not played for the Wallabies since seriously injuring his knee in the third-place playoff against Wales at last year's World Cup, coincidentally at Eden Park where Saturday's Test will be played.
With Cooper returning at number 10 to link up with Genia, Berrick Barnes has been shifted to inside centre and Beale has been left out of the starting XV, while Adam Ashley-Cooper moves from wing to full-back to accommodate Drew Mitchell.
The Test will mark Mitchell's first run-on match since the World Cup after he was in the 22 last week in Sydney but not used.
Selectors have opted against finalising their bench because of an undisclosed injury concern, meaning 25 players will travel to Auckland before a final 22 is named, so Beale could yet be involved.
With flanker David Pocock sidelined after undergoing knee surgery earlier this week, selectors have turned to Genia to lead the team. He has done so once previously, against the United States at the World Cup.
Pocock's absence, which comes after incumbent skipper James Horwill was injured before the June Tests against Scotland and Wales, means Brumbies flanker Hooper gets his first opportunity to start, at openside flanker while Ben Alexander replaces Sekope Kepu at tighthead.
While Hooper will be playing his fourth match, reserve hooker Stephen Moore is poised to draw level with Jeremy Paul as the most-capped Wallabies hooker in history, currently sitting on 71 caps.
The All Blacks are coming off a 27-19 victory over the Wallabies at ANZ Stadium.
Australia team: Adam Ashley-Cooper; Drew Mitchell, Rob Horne, Berrick Barnes, Digby Ioane; Quade Cooper, Will Genia; Benn Robinson, Stephen Moore, Ben Alexander, Sitaleki Timani, Nathan Sharpe, Dave Dennis, Michael Hooper, Scott Higginbotham.