The Redbacks's tail heaped pain on the Bulls as they moved from their overnight 8-328 to reach 485.
In reply, Queensland made a wobbly start to be 1-25 at tea at Cazaly's Stadium.
Test discard Matthew Renshaw was the only Queensland wicket to fall, trapped lbw by Chadd Sayers for 4.
They ended the day's play 4-123 and 362 runs behind the Redbacks after David Grant, Adam Zampa and Joe Mennie all contributed.
Carey's confident innings was the highlight of the day with the Test aspirant hitting 139 and scoring exactly 100 on day two.
Carey's first century, scored in his 23rd match, was joyously celebrated and included 12 fours and two sixes.
The wicketkeeper found a valuable ally in Test squad member Sayers who also hit a career-best with an intelligent knock of 46.
The pair batted through the morning session to share a 117-run stand for the ninth wicket.
Carey upped the ante after Sayers' dismissal, adding a further 45 for the final wicket alongside No.11 David Grant who contributed 8 not out.
Part-time spinner Marnus Labuschagne (3-85) mopped up the final two wickets, while leg-spinner Mitch Swepson ended with 5-142 but was unable to add to his overnight wicket haul.
Travis Head had laid the foundations for a good score on day one with an aggressive 132.