Queensland, who were bowled out for 354, dropped three catches including two off one Shane Watson over to allow WA to go to stumps at 298-6 on Friday with Marcus North unbeaten on 71 and Steve Magoffin one not out.
The match is hanging in the balance with WA (36 points) chasing an outright victory to host next weekend's final after NSW (36) claimed first innings points against Victoria in Sydney on Friday.
Queensland (40) need only to draw the match to host their sixth final in seven years.
A 118-run second wicket partnership between Chris Rogers (83) and Murray Goodwin (57) gave WA a solid platform.
NSW made a strong bid for an outright win over Victoria and a possible place in next week's final after gaining the upper hand at stumps on day two.
Victoria were 170 for four to hold an overall lead of 47 runs, but have only six second-innings wickets left.
Earlier Victoria bowled out NSW for 292 in reply to their first innings of 169 with Phil Jaques topscoring with 116.
In the other match, South Australian opener Shane Deitz scored a century in just his second match of the season to help SA seize the upper hand over Tasmania on day two at Adelaide Oval.
At stumps in the battle to avoid the wooden spoon, SA were 242 for three, in reply to Tasmania's 319, needing just another 78 runs for first innings points.