The Warriors resumed the second day 5/296 and it was young allrounder Cameron Green (126) who continued to defy the West End Redbacks with his second first-class century.
The Redbacks took 2/35 with the dismissal of Green who was trapped lbw by Zampa (3/121), but the Warriors then added 102 for the last wicket to end their innings just before tea at 8d/492.
In response, South Australia was led gallantly by opener Henry Hunt (36 off 88) after his partner Jake Weatherald fell cheaply for 15.
Hunt and Callum Ferguson added 45 for the second wicket, but when the veteran batsman edged behind for 27, the Redbacks lost 4-24.
Allrounder Stoinis snared the scalps of Hunt and Harry Nielsen (6), while Joel Paris, Matt Kelly and David Moody took one wicket each.
Debutant Liam Scott was cruelly run out in the last over before stumps, leaving SA 6/124, 368 runs in arrears of WA.