South Australia 314 & 352 for 9 (Carey 123*, McSweeney 72, Whitney 3-62) lead Queensland 308 (Peirson 94, McDermott 52) by 358 runs
A declaration appears likely overnight, with paceman Jordan Buckingham unbeaten at the crease alongside Carey.
As at the close of play, Carey is averaging 122 across four knocks this summer in positive signs for an Australian middle order missing Cameron Green for the five-Test series against India that begins next month.
Unfazed by the second new ball, Carey notched his second century of the summer by blasting paceman Mark Steketee for three consecutive boundaries in the final hour of play on Tuesday.
The 33-year-old bookended a huge six over deep mid-wicket with a pair of fours past extra cover to race through the nervous nineties and into triple figures. He capped a brilliant day at the crease by slogging his favourite victim Steketee for six over deep mid-wicket in the final over.
Carey raised his bat from only 67 deliveries, signalling his intentions to pick up where McSweeney had left off before Usman Khawaja caught the South Australian captain at first slip off Mitchell Swepson.
Whitney backed up his five-wicket haul from the first innings with three key scalps early on day three before a minor heel injury prevented him from bowling as Carey kicked on in the afternoon.
Whitney trapped opener Conor McInerney lbw early on day three, before cleaning up Nathan McAndrew’s middle stump with his first ball following lunch after the nightwatcher stubbornly stuck around through the first session.
Whitney’s figures of 8 for 119 across the two innings were the third-best for a Queensland debutant in Sheffield Shield history.
In the spotlight since his omission from the Australia A squad, Test hopeful Matt Renshaw grabbed a headline moment late on day three – but not with the bat.
The towering Renshaw dived at mid-wicket for a brilliant catch to dismiss Jake Lehmann from Marnus Labuschagne’s part-time leg-spin.
Labuschagne joined would-be Test opener Renshaw on the highlight reel with a catch above his head to send Liam Scott packing and help Queensland tear into the bowlers.