The Bulls started play on the final day at 1-26 in their second innings, needing just another 56 for victory.
Jack Clayton (34no) and Usman Khawaja (33no) ensured there would be no miracle comeback from Tasmania.
The result ended Tasmania's hopes of reaching the Shield final, leaving them last on the table with just one match to come - against NSW.
Queensland are still alive and kicking, with the Bulls to finish the round as high as second or as low as fourth.
Even if the Bulls drop to fourth, they still have a chance to reach the final if they can beat ladder leaders South Australia in the final round.
Khawaja helped set up Queensland's big win over Tasmania by scoring 127 in their first innings total of 9(dec)-425.
Tasmania were rolled for 161 in reply, with man-of-the-match Michael Neser snaring 6-37.
The Tigers were forced to follow-on, and although their second-innings total of 345 was much better, the 82-run victory target wasn't nearly enough to pose Queensland any problems.
"Maximising that new ball (was the key), that new ball nipped around a bit," Neser said.
"And then it went dead and it was a lovely batting wicket.
"It was a no-brainer to (enforce the) follow on. That wicket was getting flatter.
"The way Uzzie batted was superb. He set the game up for us."
Queensland's win over Tasmania was a perfect response from their recent flop at the WACA, where they were thumped by an innings and 12 runs by Western Australia.
"We have a massive game in Adelaide now. It's going to be tough there," Neser said.
"We know it can be flat at times, so spin will be a huge factor for us.
"Going in with a win is massive for us, so hopefully we can carry that momentum through."
Tasmania opener Jake Weatherald rued his team's poor batting display.
"If we had got (a lead of) 200, 230, we would have been a good chance," Weatherald said.
"We're just not batting or bowling well enough.
"Michael Neser was just too classy. He bowled very well throughout this game in good batting conditions."
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