Chasing 331 to win after a South Australian declaration, Queensland bunkered down and had reached 3-125 off 42 overs when play was called off at Cazaly's Stadium.
Matthew Renshaw cast aside a first-innings failure to defy the Redbacks' push for victory with a stoic 51 not out.
Queensland were very briefly threatened at 3-82 midway through the final session but injury returnee Sam Heazlett helped steady the ship with 22 not out.
Seamer Chadd Sayers, who was released from Australia's Test squad to play in the match, impressed with the ball taking 2-13 from nine typically tight overs.
Earlier, SA batted well into the middle session holding back their declaration until reaching 7-234.
Resuming at a shaky 2-59, the Redbacks were able to steady the ship thanks to half centuries from Travis Head (65) and Callum Ferguson (59).
Queensland had made a sporting declaration during the final session on Tuesday, 96 runs behind their opponents at 5-389.
Joe Burns scored a career-best 202 not out in the Bulls' first innings but only lasted a few overs the second time around, dismissed by Sayers for just 4.