The Tigers were 5-221 at the close with all-rounders Matt Johnston (3) and Luke Butterworth (9) the not-out batsmen.
Chasing the Bulls’ total of 205, the home side was never really threatened during the chase with Test opener Ed Cowan playing the sheet-anchor role with a well-made 82.
He successfully steered the home side into the lead with a miscued pull shot but fell a short time later, within sight of his third Bupa Sheffield Shield century of the season, when he spooned a limp drive to Joe Burns at cover off the bowling of Ben Cutting (2-57).
Cowan had teamed with Mark Cosgrove (67) in a 95-run partnership that put the home side in a commanding position, but the duo fell in quick succession with the heavy lifting already done.
Cosgrove was dropped twice but looked the more fluent of the pair, stroking 11 boundaries during his knock, but was run-out when called through by Cowan in search of a single to put the Tigers into the lead.
It was a much-needed breakthrough for Queensland with Cutting the only multiple wicket taker on a day where the Bulls’ quicks failed to fully capitalise on a green-tinged wicket and heavily overcast conditions.
Cutting was the shining light in the Queensland batting innings, too, his 79-not-out pivotal in their scramble from 8-89 to the more respectable 205 all out.
Resuming at 9-195 the visitors added 10 runs in the opening overs before Jackson Bird picked up his sixth wicket when he had Alister McDermott adjudged LBW for 13.
The covers went down during the innings break and approximately an hour was lost to rain but the day was otherwise uninterrupted until umpires decided the growing gloom over Blundstone Arena was making play dangerous at 5.50pm.