Chasing 297 for victory off 38 overs, Queensland finished at 7-290, meaning the match ended in a draw.
Opener Joe Burns made 103 off 142 balls, while Marnus Labuschagne made 72.
The Bulls needed 50 runs off the last 39 balls, and that equation became a manageable 34 off 32 courtesy of Charlie Hemphrey (60 off 52 balls).
But some tight bowling from WA captain Mitch Marsh (2-49) and Matthew Kelly (5-60) at the death denied Queensland victory.
The Bulls needed 12 runs off the final over, but Kelly restricted them to just five runs.
Renshaw, who was dropped from the Australian Test team on the eve of the Ashes, made just seven off 22 balls before edging Kelly behind.
Earlier, WA batsman Ashton Turner cracked 101 off 160 balls to lift the Warriors to 8(dec)-306 in their second innings.
The Warriors were in all sorts of trouble after losing 3-5 early on Monday to slump to 8-196 - an overall lead of just 186.
But Turner and Jason Behrendorff (39no) combined for an unbeaten 110-run stand to guide WA out of trouble.
Behrendorff, who is nursing a back injury, didn't bowl on either Sunday or Monday.
The 27-year-old is struggling with pain stemming from the scar tissue of an old stress fracture in his back.
His absence meant Marsh made an unexpected return to competitive bowling.
Marsh, who underwent a shoulder reconstruction in March, wasn't due to bowl competitively again until WA's next Shield match against Victoria.
But with Behrendorff sidelined, Marsh stepped up to the plate and helped put the brakes on Queensland just as the visitors appeared set for victory.
On the eve of the match, Behrendorff revealed he had been told the fracture will never fully heal - a situation some other pace bowlers have also dealt with during their careers.
Behrendorff hopes the injury won't force him to give up long-form cricket, but his inability to finish the Shield match will raise further questions about whether he should consider becoming a white-ball specialist.