Set a mammoth 422 for victory and having been skittled for 154 in their first innings, SA could have been forgiven for merely batting for survival at Adelaide Oval.
Things looked even bleaker for South Australia when Jhye Richardson dismissed Jake Weatherald for 24, leaving the home side at 1-42.
But South Australia aren't the two-time defending champions for no reason.
Opener Mackenzie Harvey plundered an unbeaten 90 off 132 balls and Nathan McSweeney (57no off 132 balls) provided the stability at the other end as the pair survived for the rest of the day to give South Australia a genuine shot at victory.
SA need a further 240 runs with nine wickets still in hand.
The biggest successful run chase in Shield history is the 6-506 SA posted to pull off victory against Queensland in 1991/92.
And SA can add another memorable chapter to their rich history if they can get over the top of WA on Saturday.
WA entered day three at 6-79 in their second innings and with an overall lead of 331.
Handy lower-order knocks from spinners Ashton Agar (48) and Corey Rocchiccioli (28) ensured WA reached 169, giving them a lead of 421.
Agar's 101-ball resistance was finally brought to an end when he was bowled by part-time spinner McSweeney.
Paceman Brendan Doggett (4-51) was the pick of the SA bowlers, while Liam Scott (2-22) and Wes Agar (2-34) also chipped in with multiple wickets.
Earlier in the match, WA set up a position of dominance by compiling 5(dec)-406 in the first innings, with opener Cameron Bancroft (186) and Jayden Goodwin (108) setting the foundations as the visitors reached 1-257 by late on day one.
A total of 18 wickets fell on a chaotic day two, with Richardson unleashing an inspiring opening spell as SA were skittled for 154.
But day three belonged to SA, and with only light rain forecast for Saturday, the Shield clash looks set for a result one way or another.
