On the back of a composed 70 from former Test opener Joe Burns, the Bulls passed their target of 156 shortly after tea on Monday.
Skipper Usman Khawaja (28 not out) hit the winning runs as Queensland secured back-to-back wins to start their Shield campaign.
"We kept saying that we needed to invest time into our innings and those run chases can really speed up towards the back end," Burns said.
Burns contributed the lion's share of the scoring in an 82-run opening stand with Australia incumbent Renshaw, who faced 109 balls for a laborious 19.
He was caught behind after lunch by Matthew Wade trying to leave Gabe Bell, who then had Burns chopping on shortly afterwards.
Bulls all-rounder Michael Neser picked up two wickets in Tasmania's second innings to go with career-best figures of 6-57 on day one, as the Tigers were bowled out for 186.
Queensland were restricted to 181 in reply, with fringe Australia seamer Jackson Bird (3-51) the pick of the bowlers.