A low-scoring contest was turned on its head as Short mastered the tricky Junction Oval pitch to score 119 - a tally nearly three times better than any other batter in the match.
The century continues a rich vein of form for Short, who broke through for his first 50-over century last week, more than seven years after his senior debut.
The Vics ended the day at 8-285 for a massive 340-run lead that seemed highly improbable just 24 hours earlier.
South Australia's lower order capitulated earlier in the day. Having resumed at 5-75, they were dismissed for 114 to concede a 55-run first-innings deficit.
Short played a major role in building that advantage, with his 70 off 69 balls on day one more than double the next best for either side in the first innings.
In the second innings, he punched 15 boundaries and a six in his 135-ball knock of 119, and it took some fancy footwork to dismiss the Vics' No.5, with Jordan Buckingham taking a juggling catch on the boundary rope.
Short's wicket earned Spencer Johnson a five-wicket haul, with the debutant paceman returning figures of 5-72.
At the time of his dismissal, Short had, incredibly, scored some 36 per cent of the runs in the match across the three innings.
Batting seemed much simpler during the latter two sessions of the day, highlighted by an 82-run stand - easily the largest in the match - for the seventh wicket between Short and Will Sutherland (43).
The news wasn't so good for returning short-form star Glenn Maxwell, who was clean bowled second ball after playing an expansive drive off Wes Agar.
Maxwell made just five in the first innings, though his dismissal came via a contentious lbw decision.
Earlier, in his first game back after suffering a broken leg, Maxwell left the field during SA's innings after being struck on a wrist by a ball when fielding at slip.Â
