The home side's batting failed to fire on Thursday at Gliderol Stadium, being dismissed for just 201.
Rookie opener Conor McInerney top-scored for SA with 51, but his dismissal left the Redbacks deep in trouble at 6-120 in reply to WA's 355.
Captain Travis Head (31) and wicketkeeper Alex Carey (25) were the only other SA batsman to pass 20.
New left-armer WA paceman Liam Guthrie did the bulk of the damage taking four of the six top-order scalps in his third Shield match, before finishing with the innings with 4-59.
WA pushed home their advantage in the final hour with D'Arcy Short unbeaten on 56 and Ashton Turner also still at the crease on 39.
South Australia began the match marginally behind Western Australia at the bottom of the standings and needing a win to avoid finishing last.