The Bulls didn't shirk from the task of both restricting the Tigers batting scoring output as well as taking wickets, never letting the home team get a firm hold on the game.
Tasmania was dismissed for 252 in their second innings, setting the Bulls 310 to win with time this evening and a full day of play tomorrow to get the target.
At stumps, the Bulls were 0-38, needing a further 272 runs for maximum points and to extend their lead at the top of the Shield ladder after second placed NSW were beaten by Victoria earlier in the day.
While Jordan Silk and Jake Doran each notched half centuries, the Queensland attack again hunted as a pack.
Impressive young paceman Xavier Bartlett broke the innings open with the wickets of Doran and Test captain Tim Paine on the way to a fine haul of 4-59 from 19 overs, while spearhead Mark Steketee cleaned up the wagging tail to claim the final three wickets for a tally of 3-59.
Allrounder Jack Wildermuth finished with 2-31 and paceman Brendan Doggett had 1-64 while left-arm spinner Matthew Kuhnemann was probing throughout on the way to 0-34 from 14 overs.
Street took two catches in the gully, one a sharp chance to claim Beau Webster and the other a one-handed screamer off Steketee that removed lower order hitter Jarrod Freeman.
Street was positive in the chase, finishing 21 not out as he and first innings century-maker Joe Burns (13no) saw the Bulls safely to the end of the third day.