Queensland 304 (Peirson 115, Abbott 5-76) and 1 for 35 need 198 more runs to beat New South Wales 320 and 216 (Dwarshuis 48*, Steketee 3-36, Sinfield 3-46)
Queensland need to score less than 200 runs with nine wickets in hand to secure an important Sheffield Shield win and condemn traditional heavyweights New South Wales to their longest-ever winless run.
Queensland ended day three at the Gabba at 1 for 35, and require another 198 runs on the final day for a victory that would secure them a share of second place with two rounds remaining.
Opener Joe Burns and debutant Aryan Jair will resume at the crease for Queensland in the morning.
The day commenced with Queensland adding 22 runs after resuming at their overnight 8 for 282, eventually conceding a 16-run deficit on the first innings.
Captain Jimmy Peirson failed to add to his overnight score and was dismissed in the second over of the day for 115. Abbott claimed both wickets to end with 5 for 76.
There were numerous starts among NSW's top-order with contributions from Blake Nikitaras (39), Kurtis Patterson (28) and Moises Henriques (40) but a steady flow of wickets and a middle-order collapse left the visitors on the brink at 8 for 158.
Queensland opening bowler Mark Steketee picked up 3 for 36, while debutant spinner Jack Sinfield impressed with 3 for 46.
Bottom-placed NSW are yet to record a win in seven rounds with their winless streak stretching into last season.