Carey came to the crease with the Aussies in peril chasing 303 to win at Old Trafford, and struck 106 off 144 in a comeback win for the ages.
Carey combined with Glenn Maxwell for Australia's highest-ever sixth-wicket stand of 212 after Australia was 5/73, and it was the highest score for any wicket against England in England.
The two led Australia almost to the end before Mitchell Starc finished the job in the last over of the game, including a six from his first ball, chasing down England’s 302 with two balls to spare.
Carey and the Aussies ended England’s unbeaten four-year, 13 Series unbeaten run.
2020 Tour of England
First T20: England won by two runs
Second T20: England won by six wickets with seven balls to spare
Third T20: Australia won by five wickets with three balls to spare
First ODI: Australia won by 19 runs
Second ODI: England won by 24 runs
Third ODI: Australia won by three wickets with two balls to spare