At stumps on day three Queensland are 2-170 in their second innings, still requiring another 301 runs for an improbable win, but giving the Redbacks plenty of headaches.
The hosts, rolled for just 135 in their first innings, made a solid start to their second with openers Joe Burns and Luke Pomersbach adding 118 before the first wicket fell.
Pomersbach was the man dismissed, miscueing a Chadd Sayers (1-39) delivery to Redbacks' skipper Johan Botha to be out for 47.
Burns made a quickfire 72 but joined Pomersbach in the dressing room just eight runs later when he was caught off the bowling of former South African international Botha (1-36).
Former Test batsman Usman Khawaja (26no) and Nick Stevens (24no) reached stumps unbeaten and will resume on Saturday with hopes of pulling off an unlikely victory.
Earlier, Callum Ferguson scored an unbeaten 70 as the Redbacks added 180 runs to their overnight score to reach 6(dec)-202 just after lunch.
Ferguson shared a 91-run, 103-ball stand with Botha (40) after the Redbacks had lost four wickets in the morning session.
That partnership allowed the visitors to close the innings with just under five sessions remaining in the game as they bid for an outright win which would boost their hopes of a first Shield title since 1995-96.
Bulls skipper James Hopes was the only Queensland bowler with multiple wickets, finishing with 2-47 in the truncated Redbacks' innings.