Carey top-scored with 103, the highest score of the final so far, as SA were bowled out at tea for 258 on Sunday at Junction Oval.
The Test 'keeper was the last wicket to fall, caught by Peter Handscomb at first slip after trying to ramp Fergus O'Neill.
Carey brought up his ton as he tried to farm the strike to protect No.11 Jordan Buckingham.
Buckingham provided valuable late resistance and was 10no, while Scott Boland took 3-78.
SA's late-innings fightback - they were 7-122 before lunch - ensured the final will go into day five.
McAndrew made 60 in a 105-run stand with Carey for the eighth wicket - the highest partnership so far in the final - before Victorian captain Will Sutherland made the breakthrough.
McAndrew played back and the ball kept low, skidding onto his stumps. McAndrew faced 144 balls and hit six fours and a six. Â
Carey hit six fours and a six in his commanding 168-ball knock.
SA started day four on 5-94 and reached 7-204 at lunch, an impressive recovery given Boland had threatened to run amok.
Four overs into play on day four, Carey was lucky to survive when an inside edge off Boland went down fine leg for four.
The next ball was driven for a much more convincing boundary, before a single put Liam Scott on strike.
Scott was given out lbw, with the ball hitting his back leg and the batsman shaking his head in disapproval as he trudged off the ground.
The next ball, a brute of a delivery had Ben Manenti caught behind to end the over. Carey survived Boland's hat-trick ball at the start of his next over.
Carey and McAndrew then dug in to first deny Victoria a quick kill and then start to swing the game back towards a much more even contest.
There is plenty of life in the Junction Oval wicket and the home side are set for a nervous run chase as they aim for their first Shield title since 2018-19.
SA must win to successfully defend their title.
In a absorbing final with several plot twists already, SA will fancy their chances of knocking over Victoria cheaply.
Three overs before lunch, McAndrew was given a life when his edge off Boland somehow was not snared by either Sutherland at first slip or Peter Handscomb at second.
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