Jhye Richardson (1-47) dismissed South Australian opener Callum Ferguson (127) with seven balls left in the match, which secured a thrilling victory.
The win lifts WA to the top of the standings, having completed their fixtures, but will wait on the result of Queensland's match tomorrow to see if the final will be hosted at the WACA Ground.
After being bowled out for 252, WA had the Redbacks in all sorts of trouble at 5-76 and 9-190.
But a 56 run stand for South Australia's tenth wicket took the game down to the wire.
Nathan Coulter-Nile did most of the damage for WA as he claimed 5-46 including three top-order scalps.
Western Australian's Middle-order batsman Hilton Cartwright scored 41, but a dashing 86 from highly regarded all-rounder Cameron Green provided the back bone to the visitors' innings.
Green swung the bat late in the innings as wickets fell with his runs coming off 78 balls and featured three sixes.
WA spinner Ashton Agar copped a nasty blow to the head whilst attempting a catch late in the game.
"Ash is recovering well and is in good spirits after an impact to the face," Sports Science Sports Medicine Manger Nick Jones said.
"He's been diagnosed with a low grade concussion and will require some stitches to repair the wound on the bridge of his nose."
Details of who WA will play in the final and where will be finalised this week.
17 November 2019