After posting a rapid-fire 90 in the first innings at Cricket Central, Carey pulled South Australia back from the brink with 111 runs from 158 deliveries in the second on day four.
The two knocks combined to mark his most successful start to a Sheffield Shield season since his Test debut in 2021.
Carey's efforts came after he finished last summer with an unbeaten 98 against New Zealand, and will be reassuring for an Australian side preparing to lose Cameron Green for at least part of the summer through his back injury.
"There's some positive signs there," said Carey of his first match since returning from the white-ball tour of the UK.
"I felt good with the bat, felt good over in England so it's nice to bring some of that form home.
"I'm very excited (for India). They're right up there with the best team in the world at the moment across all conditions. It'll be a great opportunity for us."
Nathan McSweeney joined the runfest with a century as he and Carey added 182 for the fifth wicket. (Steven Markham/AAP PHOTOS)
On Friday, Carey steadied the ship after Test teammate Nathan Lyon (3-94) showed his own form by sparking a collapse of 4-9 as the visitors chased 389 for victory.
Lyon tickled the off-stump of Travis Head (10) in the most significant of three early wickets, with nightwatchman Nathan McAndrew (2) and Conor McInerney (0) joining the superstar batter in the dugout courtesy of the spinner.
Carey came to the crease just as South Australia needed a hero at 4-23 and forged a 182-run partnership with captain Nathan McSweeney (127no from 283 balls), who carved out a brilliant century of his own.
The gloveman struck a blow in his tit-for-tat with Lyon by sweeping the veteran past deep mid-wicket for his ninth four of the innings to reach his half-century, which guided South Australia into triple figures and relative stability.
Just after lunch, Carey notched a seventh first-class century with a single to deep cover off Liam Hatcher (0-62).
Ollie Davies dropped Carey at point on 110 but Blues captain Moises Henriques helped the 23-year-old save face by catching Carey in the cordon from Tanveer Sangha's bowling after he added only one more run.
Nathan Lyon looked in strong form with three wickets. (Steven Markham/AAP PHOTOS)
McSweeney picked up where Carey left off but with their tail unlikely to wag, South Australia looked reluctant to take the game on late, despite having five wickets in hand.
Carey said the target of 389 was "probably just a little bit out of our reach".
"I guess if you go a little bit harder early, you open the door to a Test spinner and a good attack, then things could have gone against us," he said.
Lyon could not repeat his early heroics as Henriques threw batter Nic Maddinson the ball late on when it was clear no result would eventuate.
"It definitely feels like one that got away when you only take one wicket in the last 90 overs of the day on day four," Henriques said.
"It's a hard one to cop, when you're so far in front of the game and have them 4-23.
"It feels a lot more than the one that got away, to be honest."
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