Burns carved out a career-best 202 not out as the Bulls fought back in unlikely fashion on day three.
Queensland were able to declare their innings at 5-389, a deficit of 96 runs.
At the close South Australia had reached 2-59 through Callum Ferguson and Travis Head, who now lead by 155 runs.
Queensland recommenced at 4-123 looking at a potentially massive first-innings deficit, however Burns and Jack Wildermuth (56) began to rebuild by adding 104 for the fifth wicket.
Young captain Jimmy Peirson continued the fightback with a steady knock of 82 not out and contributing to an unbroken 186-run stand for the sixth wicket.
Burns upped the ante after passing 150 eventually hitting 15 fours and four sixes to surpass his previous highest first-class score of 170.
Leg-spinner Adam Zampa (2-138) shouldered the bulk of the responsibility on a wicket said to be "breaking up a little bit" into the final day.
Young quick David Grant also played a tidy part with figures of 1-38 off 17 overs, including six maidens.