In reply to the Redbacks' 7-259, Victoria reached the victory target with 26 balls to spare thanks largely to Harris, who struck an unbeaten 102 off 105 deliveries.
Harris brought up his century on the final ball of Tuesday's match when he lofted spinner Lloyd Pope down the ground for four.
Mackenzie Harvey (61 off 71 balls) and Peter Handscomb (45 off 29 balls) also produced handy knocks for Victoria, but it was Harris who was the star.
The 29-year-old, who lost his spot in the Test team during the Ashes but has been named for the tour of Pakistan, finished with six fours and three sixes in a man-of-the-match display.
"I don't think I've played a one-day game for Victoria since this time last year, so it's been a little while," Harris said.
"Everyone batted really well, so I just jumped in behind Mackenzie Harvey and then Peter Handscomb, and a few things went my way.
"I feel like I batted well in the Shield game and batted well again today. It's good to spend some time in the middle.
"We've still got another Shield game before we go away (to Pakistan), so that will be good."
The result kept Victoria in the hunt for a spot in the domestic one-day final on March 11.
The Bushrangers have now posted a win, a loss, and a no-result from their three matches and they have three more games to play.
South Australia slumped to the bottom of the table with just one win to show from five matches.
The Redbacks' total of 7-259 was about 50 runs short of where they wanted to finish.
Nathan McSweeney (53) and Jake Lehmann (49) made promising starts but the loss of 3-20 saw the Redbacks wobble to 6-189.
Liam Scott (42 not out off 33 balls) unleashed late in the innings to lift the home side to a defendable total, but Victoria were in control throughout the run chase.
Pope finished with figures of 3-51 for South Australia, while McSweeney (1-32 off 10 overs) was the most economical bowler.
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