The hosts, who led by 20 on the first innings, made 341 to set the Bulls 362 runs for victory.
Big guns Matt Renshaw and Marnus Labuschagne were still at the crease at stumps on Monday with Queensland 1-20 in their second innings.
Kuhnemann, who had taken 3-14 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 six his best score there.
Tasmania resumed day three at 5-153 and took the game away from the Bulls.
Captain Jordan Silk had failed to reach double figures in his previous three Shield innings but top-scored with 81.
Wicketkeeper Jake Doran continued his strong match, making a polished 76 to go with his first innings knock of 31.
Kuhnemann and Doran added 97 for the sixth wicket to put Tasmania firmly in charge.
The Bulls have struggled with the bat in recent matches and will need hundreds from Renshaw and Labuschagne to have any chance of an unlikely victory.
Renshaw already has three tons this year for the Bulls and Labuschagne has two.
