After Carey and Nathan McAndrew led SA out of trouble on day four at Junction Oval, Victoria lost two crucial wickets in the last 20 minutes on Sunday.
SA will go into day five with the momentum, but after a succession of plot twists already in the final the result is too close to call.
Victoria will resume on 5-102 on Monday against the reigning champions, with nightwatchmen Mitch Perry and Todd Murphy yet to score.Â
They need another 94 for their first Shield title since 2018-19 and have Oliver Peake and captain Will Sutherland yet to bat.
Carey also scored a ton in last year's Shield final win, and his game-high 103 against the Victorian attack, led by his Test teammate Scott Boland, could prove the difference this time.
Asked where it ranked among his Shield centuries, the Test keeper replied: "Ask me after the game."
"Scotty Boland in front of Victorian fans, it's a pretty tough battle," Carey said.
"I want to win another Shield ... I have a lot of pride for these colours.
"I guess it goes a bit more back to the footy days, state versus state - State of Origin.
"Yeah, if it means we beat the Vics it's pretty exciting."
But Victorian coach Chris Rogers remains confident.
Former greats Simon O'Donnell and Cameron White spoke to the Victorian team before the final and Rogers has drawn on their advice.
"What I took out of it was it was going to be an arm-wrestle and it was going to feel bad at times," Rogers said.
"It's played out exactly that way."
Boland was on a hat-trick before lunch, and at 7-122, only 63 in front, SA were on the brink.
But Carey and McAndrew combined for a 105-run stand that meant SA reached 258 and set up a tricky 196-run target for the home team.
McAndrew, who made 60, then took two early wickets as Victoria slumped to 3-35, before old hands Peter Handscomb and Marcus Harris steadied the victory chase.
Henry Thornton had Handscomb caught behind for 28 and Liam Scott removed Harris in the next over for 35, putting SA right back in the contest.
"They're big wickets - we still have five to get, but it sets up for a great finish," Carey said.
But Rogers is far from discouraged.
"We've been in these situations before and come out on top," he said.
"We still have a lot of batting left in the shed, so we have to believe we can get it done."
Rogers agreed that batting became easier for SA, the longer their second innings progressed.
"The 'air' felt like it got taken out of the ball a little bit and it became a bit easier to bat ... that's what we hope is going to happen," he said.
Rogers also heaped praise on Carey for his game-changing knock.
"He played beautifully ... what more would you want from your star player. He's a big-time player and he stood up," he said.
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