Set 332 for victory, WA remained on the required run-rate throughout the day before being dismissed for 222 with little over an hour remaining in the match.
The 109-run win is the second in succession for the fourth-placed Redbacks, who have put themselves back in contention for a berth in next month's Shield final with three rounds to play.
At 5/188 after tea, Western Australia looked capable of pushing for a win or at least holding on for a draw.
But Worrall had other ideas, capturing all five remaining WA wickets for 34 in his return to four-day cricket.
Player of the Match Worrall ended up with figures of 5/31 from 18 overs, notably clean bowling WA's last hope Josh Inglis (28) with a superb delivery.
There were also key contributions earlier in the day from Nick Winter (2/63) and Wes Agar (2/52) who, along with swingman Chadd Sayers, also bowled superbly throughout the contest.
Left-armer Winter picked up Cameron Green for 15 and then produced a sublime delivery to have dangerman Marcus Stoinis LBW for 60.
The morning session saw young paceman Agar dismiss Cameron Bancroft and Shaun Marsh in successive balls after the WA openers had laid a solid platform.
Bancroft followed up his three-hour 25 in the first innings with a more evenly-paced 19 before he was caught behind by Harry Nielsen, while Marsh went the same way for a golden duck.
South Australia opened the day by extending their innings by just two overs, adding 17 runs before declaring at 5/196.
Western Australia slip to third in the ladder, with Queensland grabbing second spot thanks to its resounding win over Tasmania on Sunday.
The Redbacks next confront Shield leaders New South Wales in Bankstown from Monday, 24 February.