Victoria, still raw with shock after the death of former Test batsman David Hookes in a brawl outside a Melbourne hotel last month, were aided by the bowling of paceman Allan Wise who captured a career best 5-47.
Chasing 354 to win on Wednesday, South Australia started the day at 75 for two with skipper Darren Lehmann and Greg Blewett at the crease and carrying their state's hopes. But South Australia suffered a dreadful collapse of 81 for eight to lose the game before lunch. Wise's fellow left-arm paceman Mathew Inness finished with 4-26.
South Australia had made 262 in the first innings in response to Victoria's 343 and were all out in its second innings for 156, in reply to Victoria's 272.
The win took Victoria 12 points clear at the top of the Sheffield Shield table, meaning first innings points in any one of their remaining three games will clinch a home final.
In Brisbane, defending champions New South Wales lost all hope of retaining the Shield despite a breathtaking century by Phil Jaques as the match with Queensland ended in a tense draw .
Set 327 from 55 overs to win in its second innings of a rain-affected match, New South Wales mustered 277 for eight with Man of the Match Jaques blazing a run-a-ball 146.
In Hobart, Western Australia's Marcus North remained unbeaten on 118 as the visitors closed the first day's play at 345 for four in the match against Tasmania.
New South Wales struggle against Queensland