Needing five wickets for victory on the final day of play, the West End Redbacks quickly dismissed Bulls wicketkeeper Jimmy Peirson for 27 and piled pressure on the remaining Queensland batsmen.
Chadd Sayers found movement in particular off the Gabba pitch with several close appeals throughout the morning.
But Bulls batsman Marnus Labuschagne eventually steered his side to the target total of 150, finishing unbeaten on 72 to secure Queensland’s first Shield win of the season.
Redbacks’ swing bowler Nick Winter backed up a four-wicket first-innings haul with 4-37 in the second innings.
Debutant Wes Agar also impressed with another two wickets on top of his own four-wicket first-innings performance.
South Australia will remain up north and confront Queensland again in the next round of the Marsh One-Day Cup on Wednesday at the Gabba.
The Redbacks then host their first home Shield match of the summer at Adelaide Oval against New South Wales from 1 November.