Queensland 178 and 20 for 1 need 342 more runs to beat Tasmania 198 and 341 (Silk 82, Doran 76, Weatherald 62, Kuhnemann 56, Swepson 4-47)
Tasmania, who led by 20 on the first innings, made 341 to set the visitors 362 runs for victory. Matt Renshaw and Marnus Labuschagne were still at the crease at stumps with 20 for 1.
Kuhnemann, who had taken 3 for 14 with his spin in the first innings, made a stoic 56 off 201 deliveries. It was an innings to savour for the former Queensland star whose previous highest first-class score was 27 not out. The 29-year-old has played five Tests for Australia with 6 his best score, although was once a nightwatcher during a Test in India.
Tasmania resumed day three at 153 for 5 and took the game away from Queensland.
Play was suspended for nearly half an hour during the morning session after a fire alarm was activated at the ground with firefighters spotted in the Ricky Ponting Stand.
Queensland have struggled with the bat in recent matches and will need big runs from Renshaw and Labuschagne to have any chance of an unlikely victory.
Renshaw already has three tons this year and Labuschagne has two.