Chasing a challenging 300 for victory, SA were in big trouble at 4-108 after Henry Hunt (66) joined Conor McInerney (1), Nathan McSweeney (18) and Jason Sangha (0) back in the pavilion.
But a 148-run stand between Lehmann (105 not out off 193 balls) and Liam Scott (83 off 137) turned the match on its head, helping propel South Australia to victory.
Lehmann notched his 12th first-class century and also brought up the winning runs by striking three consecutive boundaries off Xavier Crone.
The result means South Australia will host the Sheffield Shield final, irrespective of how they fare in their final-round match against Queensland in Adelaide.
If Victoria had won, they would have finished the round as high as second.
But the loss has left them struggling for survival in fifth spot, now requiring a minor miracle to scrape into the final.
Not only do the Bushrangers need to beat WA at the WACA in the final round, they must also rely on South Australia beating Queensland, and last-placed Tasmania defeating NSW.
Victoria were all smiles early on Sunday when they made significant inroads into South Australia's top order.
McSweeney was the first batter to fall for the day, trapped lbw by Fergus O'Neill after South Australia had added just seven runs to their overnight total of 1-47.
O'Neill found the edge of Sangha two balls later as SA slumped to 3-54, and Hunt's resistance was over when he skied Sam Elliott to the deep.
But it was the Scott and Lehmann show from that point on, with the pair's partnership taking the game away from Victoria.
South Australia needed just 44 more runs when Scott fell, edging Scott Boland to slip to end his hopes of scoring a maiden Shield ton.
Lehmann was dropped on 80 by Campbell Kellaway at short cover with the score reading 5-258, and he made the most of the reprieve to guide his team to victory.
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