The victory came in the final session of the match, as the Tigers desperately fought to conjure an unlikely victory with Queensland losing four wickets after tea as the second new ball caused the tension to rise.
But an unflappable unbeaten century by captain Usman Khawaja saw Queensland home, after the classy left-hander had combined with Test batsman Marnus Labuschagne (78) earlier in the day to lay the platform for the win.
Queensland finished at 7-310, with a Jack Wildermuth flurry of 30 from 23 balls narrowing the asking target as the tension built.
His dismissal, followed by that of Mark Stektee, had Tassie paceman Nathan Ellis on a hat-trick but Xavier Bartlett was equal to the task, and stuck with Khawaja through until the end to claim the victory.
Khawaja was 115 not out from 206 balls, with his patience fulfilling a key role in the partnership with Labuschagne, who kept the score ticking along as the duo set the innings on course for the final session result.
Player of the match Joe Burns, whose mighty first innings score kept Queensland in the game, and Bryce Street were both dismissed early in the day but Queensland knew a winning result was possible if they kept composed in what were generally good batting conditions.
The Bulls now prepare to meet the Tigers in their opening Marsh One Day Cup match on Monday at Blundstone Arena before travelling back to Brisbane to host three Shield matches, with the first against Western Australia at the Gabba.