The match was called off early in the last session of the final day with the second last placed Bulls 2-135 in their second dig, with opener Joe Burns 80 not out as the hosts led by 43.
WA batsman Will Bosisto was named man of the match after his career high 167 not out helped the Warriors post 540 in their first innings while WA skipper Mitch Marsh struck 151.
Marsh revelled on the benign deck to give a not so subtle message to selectors after being overlooked for Australia's one-day series against South Africa.
He embraced the chance to regain his batting mojo at the small Allan Border Field ground - and gave the national team selectors food for thought ahead of the test series against India.
Queensland looked wobbly at 2-76 in their second dig on Tuesday - still trailing WA overall by 16 runs - when Marnus Labuschagne was trapped LBW by Marsh for 10.
But Burns stepped up with 12 fours and a six in his 85-ball stand to ensure a draw.
Earlier, Bosisto was the last man standing when WA were finally dismissed with an unlikely 92-run first innings lead.
His 377-ball knock featuring 22 fours was his second ton of his 19-game first class career.
Bosisto had shared a 185-run sixth wicket partnership with Marsh to rescue WA who were at one stage reeling at 3-42 in reply to Queensland's 9(dec)-448.
"When you see a guy put together an innings like that, it's amazing. I loved every minute batting with him," Mitch Marsh said.
"From the position we were in, with the team in a bit of trouble, it is my job to stand up in those moments, and I was pleased I was able to do that for the team."
WA head to South Australia next week for their round four clash against the Redbacks.