At stumps on day three, the Bulls are 2-208, holding an overall lead of 219 after Burns was dismissed for an impressive 102.
Stumps were called when Burns offered a difficult return catch to Bushrangers keeper Matthew Wade, who was rewarded for his unusual decision to bowl the last over of the day.
Burns - who hit 75 in the first dig - cut a devastated figure after hoping to survive the day, only to have his three-and-a-half hour innings that featured 11 fours and two sixes end.
Burns had put on a 193-run opening stand with Luke Pomersbach, who was caught behind by Wade off Scott Boland (1-47) for 85 - backing up from his first-innings 73.
Earlier a late collapse ensured Victoria were bowled out for 371 to just miss out on first-innings points.
Bulls skipper James Hopes (3-61) struck as Victoria fell short of Queensland's first-innings total of 8(dec)-382, while Alister McDermott (4-78) also impressed with the ball.
The Bushrangers would have backed themselves to pick up the two points at 7-368 and with big-hitting allrounder John Hastings still at the crease.
However, they lost 3-3 - all victims of Hopes.
Hastings (47) was the last man to fall when he holed out on the boundary to Chris Lynn.
Victoria resumed at 5-230 on Tuesday morning but lost David Hussey (77) and Dan Christian (39) in the morning session before the Hopes-inspired collapse finished off their hopes of first-innings points.
Bottom team Queensland have approached the clash as a must-win game after amassing just four points in five matches, while the second-last Bushrangers (8pts) are reeling from two outright losses.