The wet weather is likely to ensure the Sheffield Shield match, a prelude to the upcoming final between the two teams, will end in a draw at Junction Oval after 50 overs were lost to rain.
Victoria were 5-282 and on track for a sizeable first innings lead when the visitors hit back to take 5-26 and restrict them to 308.
In reply South Australia were 0-27 before play on Monday was abandoned.
South Australia captain McSweeney, who opened the batting for Australia in the 2024-25 Test series against India, claimed 3-18 with the ball.
After making the vital breakthrough to dismiss Campbell Kellaway with his offspin on day two, McSweeney cleaned up the tail on Monday to help restrict Victoria's lead to just three runs after South Australia had made 305 batting first.
Earlier in the day McSweeney took two sharp catches to dismiss Oliver Peake (59) and Will Sutherland (51) to give him three for the innings.
Peake and Sutherland added 101 for the sixth wicket. Both fell to the offspin of Ben Manenti (2-76).
The signs from this match are that the Shield final will be both a fitting conclusion to the season and a closely fought one.
South Australia showed in their title win last year and once again on Monday that they are never out of the match.
Rain is forecast until lunch on Tuesday but the afternoon session will be an opportunity for both sides to get little individual wins that may provide a psychological advantage in the five-day final which begins at Junction Oval on March 26.
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