The West End Redbacks set the Warriors a target of 243 on a lively WACA pitch but the home side chased the total down comfortably before stumps on the third day of play.
The result vaults WA into third position on the Shield ladder with two rounds remaining. South Australia remain without a win after eight matches.
Youngster Josh Philippe (53 not out) steered the Warriors to victory after Sam Whiteman (44), Cameron Bancroft (52), Mitch Marsh (31) and Josh Inglis (29) all made solid contributions.
The loss was soured further for SA with Daniel Worrall bowling just one over in the second innings before reporting hamstring soreness. He did not return to the Redbacks attack.
South Australia entered day three 8/218 with captain Travis Head looking to add to his 72 and build a defendable total.
But he fell in the opening over and the visitors were eventually all out for 240 with Matt Kelly taking a career-best 6/67.
The Warriors run chase started impressively with the only 100-run stand of the match as Bancroft and Whiteman put on 112 for the first wicket.
That set the tone for WA which steadied after both openers fell with Marsh and Inglis putting on another 61.
Joe Mennie (3/55) and debutant Luke Robins (1/90) were SA’s wicket-takers in the second innings.
Nick Winter worked tirelessly in his 24 overs without fellow swingman Worrall but went without a wicket after taking four first-innings scalps.
South Australia confronts reigning champions Queensland from Monday, 11 March to begin the penultimate round of this summer’s Sheffield Shield season.