The Bulls dominated the first two days at the WACA Ground in Perth before WA produced a stunning fightback on Saturday.
After Richardson (5-19) ran riot to bowl Queensland out for 68, WA were just 67 runs away from chasing down the 201 victory target at stumps on day three.
Richardson demanded the attention of Test selectors as Queensland collapsed to 5-13.
The 30-year-old has battled countless injuries in a stop-start international career, playing four Tests since debuting in 2019.
But a call-up will be on the cards if he is fit and firing during a busy 12-month period in which Australia will play at least 20 Tests, with chief selector George Bailey having previously admitted the nation's depth will be tested across all formats.
The odds looked stacked against WA at 5-83 after losing Cameron Bancroft (9), Hilton Cartwright (0), Joel Curtis (4), Sam Whiteman (40) and Corey Rocchiccioli (6).
But allrounder Aaron Hardie (48 not out) and paceman Mitch Paris (19 not out) combined for a 51-run partnership to give WA the edge at 5-134 when poor light stopped play.
Uncertainty remains over whether Sam Fanning can bat if called upon on Sunday after the New Zealand-born opener hobbled off with an apparent hamstring injury.
Fanning, who top-scored for WA with 64 off 149 deliveries in the first innings, grabbed at his hamstring while chasing a ball to the boundary.
The 25-year-old did not return to the field and was spotted in the lunch break on crutches.
Under Cricket Australia's injury substitution trial, teams can only replace an injured or ill player in a regular-season Shield match until stumps on day two.
It means Fanning cannot be replaced, leaving WA potentially a batter down for their run chase.
He added to WA's casualty ward after illness ripped through their camp, leading to the substitution of debutant Tom Murray on day two and Jayden Goodwin's late omission before the toss.
Left-armer Paris (3-21) struck twice in the first over to remove both openers, Hugh Weibgen and Angus Lovell, as he combined with Richardson to seize momentum.
Lachlan Hearne (11) and Hayden Kerr (22) fell in consecutive balls before lunch, with Paris and Richardson wrapping up the innings shortly after the break.
Earlier, Test hopeful Xavier Bartlett (5-48) cleaned up the tail to skittle WA for 175 in their first innings.
