Brumbies halfback Joe Powell also comes on to the bench as Phipps' back-up.
Australia claimed the first test in Brisbane 18-9, before world No 2 Ireland bounced back to square the series 1-1 with a 26-21 victory last weekend.
Tonight's decider in Sydney will be the first time the two nations have clashed in the city since 1994, when the Wallabies won 32-18 at the Sydney Cricket Ground.
Jack Conan is the surprise starter in a reworked Ireland side.
Coach Joe Schmidt has made five changes to his run-on XV, with Conan at No 8 in a rejigged loose forward trio.
Conan, 25, has played eight tests and scored four tries in his five starts at the back of the scrum.
He started on the bench in the first test loss in Brisbane but was not involved in the win in Melbourne.
His inclusion was necessitated by a sternum injury to openside flanker Dan Leavy, who misses out on the squad altogether.
It will be just the second time O'Mahony has started a test at openside flanker.
There are two changes to the front row, where loosehead prop Jack McGrath comes in for Cian Healy and mobile hooker Sean Cronin starts ahead of Niall Scannell.
In the backs, Bundee Aki returns at second-five in place of the injured Garry Ringrose (foot), while exciting young winger Jacob Stockdale is back for the crocked Andrew Conway (hip).