Chasing 267, Queensland crashed to 6-43 at Allan Border Field on Saturday before bad light ended day three.
The Bulls started the penultimate round in second spot, but South Australia's nine-wicket win over NSW has pushed Queensland down to third on the live ladder.
It means Queensland needed to go all out for victory against WA, but their batting collapse - and a terrible weather forecast for Sunday - has left their hopes in tatters.
Between 20mm to 90mm of rain is forecast for the area on Sunday, meaning a very real chance the match will end in a draw.
If the rain holds off for at least a little while, WA will be backing themselves to run through Queensland's tail on a wicket that has become increasingly tough for batters.
A draw would leave Queensland needing to beat Tasmania in Hobart in the final round and relying on South Australia losing to ladder leaders Victoria in order to regain second spot.
WA started day three at a dominant 0-132 in their second innings - an overall lead of 169 - with Sam Fanning on 82 and Cameron Bancroft 44.
Both Fanning (87) and Bancroft (72) missed out on centuries as WA were skittled for 229.
Star Bulls batter Marnus Labuschagne was the surprise destroyer, snaring 4-22 from 12 overs as WA's star-studded battling line-up crumbled.
Cooper Connolly (10), Sam Whiteman (9), Hilton Cartwright (1) and Josh Inglis (1) fell cheaply as Queensland rocketed their way back into the contest.
But the home side's joy was short lived, with Cameron Gannon (3-26) and Joel Paris (2-15) ripping through Queensland's top and middle order.
Paris claimed the prized scalps of Labuschagne (13) and Matt Renshaw (4), while Gannon sent Hugo Burdon (4), Usman Khawaja (2) and Hugh Weibgen (2) packing.
Queensland's plight was summed up just before play ended when Steve McGiffin set off for a doomed single before being sent back by Jimmy Peirson.
McGiffin was run out well short of his crease, with Peirson slumping to his knees in disappointment at the wasteful sacrifice.
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