Maher scored the bulk of Queensland's second innings total of 271, with the extras column making the second highest contribution of 22.
His knock on Thursday put Queensland in a dominant position with a lead of 339 and a day to play.
Maher opened the innings and his formidable innings only ended when he slipped and was run out by spin bowler Xavier Doherty.
Tasmania, who made 333 in their first innings, must now score at almost 3.3 runs an over for 104 overs on Friday to reach the required 340.
In Adelaide, leg-spinner Stuart MacGill will have a chance to bowl New South Wales to victory over South Australia after they secured a massive lead -- thanks in part to a dashing century from all-rounder Dominic Thornely.
New South Wales were just six wickets from an outright win heading into Friday's final day.
South Australia were 155 for 4 in their second innings at stumps, still needing another 340 for the unlikeliest of victories.
Callum Ferguson was at the crease on 70 with Nathan Adcock on 32. They had put on an unbroken 84.
But Thornely said MacGill would be hard to stop, with the pitch starting to take more turn.
Thornely continued a top season with the bat, scoring 102 from 131 balls to allow NSW to declare their second innings on 331 for 7 about an hour after lunch, with a 494-run lead.