With the final pair at the crease, Test fast bowler Ben Hilfenhaus struck a four wide of long-on from the penultimate delivery of the match as Tasmania successfully hauled in South Australia's tally of 210.
Tasmania were marginally behind the required run-rate for much of their innings but captain Tim Paine played a pivotal knock of 56 to top-score for the Tasmanians before being dismissed in the final over.
It was South Australia's third defeat on the trot and all but ended their title hopes, while Tasmania have recovered from two opening defeats to record successive wins.
Tasmania defeated the Redbacks on Wednesday, overcoming SA's season-high target of 269 by two wickets - also on the second last ball of the innings.
Peter George collected the best bowling figures for SA, knocking over Tasmania's three top-order batsmen to finish with 3-27 off ten overs.
Earlier, South Australia failed to make the most of a bright opening and after reaching 2-157 in the 35th over, they suffered a steady loss of wickets to finish all out for 210 off the last ball of their allotted 50 overs.
Opener Michael Klinger once again top-scored for South Australia with 74 and was denied a second successive century - following his unbeaten 140 on Wednesday - after he was bowled by paceman Ben Laughlin (3-33).
Fellow quick Andrew Fekete was the pick of the bowlers collecting 4-38 off his ten overs and was named player of the match.
Paine was ecstatic with the win, especially given he believed the wicket deteriorated throughout the day.
"We did brilliantly to win that game," he said.
"I thought the difference in the wicket between the first and second innings was probably 40 or 50 runs, so for us to get over the line, we've really done it the hard way.
"We are trying to be a bit more positive with our batting. It sounds simple but at times with one-day cricket you have to get bat on ball, protect the stumps and pads, and hit more balls than you don't."
South Australia fast bowler Peter George lamented his side's failure to close out the match once again.
"I think there are definitely positives that we can take," he said.
"But the reality is we are none from three at the moment so we have some work to do."