SA are 3-182 at tea on Saturday's fourth day of play in Adelaide with Sangha and Carey featuring in an unbroken 154-run partnership.
The pair came together with SA in strife at 3-28 at Karen Rolton Oval.
But Sangha, who was dropped on 13, has compiled a classy 84 not out from 147 balls and Test star Carey is unbeaten on 78 from 113 after reaching his half-century with a six.
The highest run chase to win a Shield final is Victoria's 2-239 against NSW in 1990/91.
SA, aiming to win the Shield for the first time in 29 years, slipped early as Bulls paceman Mark Steketee (2-25) and Michael Neser (1-49) made inroads.
Neser struck with the 14th ball of the innings, dismissing Conor McInerney for a duck when the left-hander edged to Angus Lovell at third slip.
Steketee, with his first delivery of the day, removed Henry Hunt for six, caught at second slip by Ben McDermott.
Steketee claimed another victim when SA skipper Nathan McSweeney (14) nicked to wicketkeeper Jimmy Peirson.
And the right-arm quick should have added a third wicket when Sangha, on 13 and the score 3-37, was dropped by McDermott at second slip when diving in front of Usman Khawaja at first slip.
Queensland were bowled out for 95 in their first innings - the lowest total of any team batting first in a Shield final - and SA posted 271 all out in reply.
The Bulls appeared down and out when 6-221, just 45 runs ahead, at lunch on day three.
But centuries from Jack Wildermuth (111) and Jack Clayton (100) triggered a comeback and Queensland reached 445 in their second innings, a 269-run lead.
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