It was the first century in Shield cricket in more than a year for ex-Test opener Burns, who produced a superb 171 to be the last batsman dismissed after scoring almost 62 percent of his team's total runs in their first innings on the second day of the match.
The Bulls were dismissed for 275, a total that looked a long way off when the side was reeling at 7-161 following a mini-collapse that started when second top score Marnus Labuschagne (49) was adjudged LBW.
Queensland trailed the home side by 57 after the Tigers were bowled out this morning for 332, with left-hander Caleb Jewell finishing with 140 from 236 balls to register a lone hand innings that Burns first emulated and then eclipsed as he batted sensibly with the Queensland tail.
Young paceman Xavier Bartlett hit 25 from 79 balls while debutant Matt Kuhnemann was patient and disciplined on the way to 3 from 28 balls as he bought Burns the time to push on from 150.
Burns faced 217 balls in his innings, hitting three sixes and 18 fours in a crisp and authoritative innings.
Earlier paceman Brendan Doggett returned the best figures of 4-88 for the innings for Queensland.