In a thrilling and somewhat controversial finish at Adelaide Oval, Pope took 6-74 to have Victoria all out for 207 in pursuit of an unlikely target of 346.
Pope took four wickets in 13 minutes to win the match, after Victoria looked likely to claim a draw with four wickets in hand and 30 minutes left before stumps.
The win marked South Australia's first win over Victoria since 2015-16, with the two teams having played 18 games since then.
But the finish was not without drama, with Victoria's Campbell Kellaway (80) given out at bat-pad among the flurry of late wickets.
Campbell Kellaway top-scored with 80 in Victoria's second innings against South Australia. (Matt Turner/AAP PHOTOS)
Kellaway appeared bewildered by the call, with replays suggesting the ball may have come flush off the pad and not hit his bat on the way to the fielder.
From there it appeared inevitable that Pope would take South Australia to victory, before he wrapped up the match by trapping Cameron McClure lbw attempting to leave the ball.
Pope's figures made for just the third five-wicket haul of his Sheffield Shield career, and his first in four years after bursting on to the scene as a cult hero in the 2017 under-19s World Cup.
Pope had always looked the most threatening of South Australia's bowlers on a deteriorating day-four wicket.
The legspinner was the only bowler to threaten Victoria's batters in the opening session, with Ashley Chandrasinghe (52) and Kellaway well set.
Henry Thornton eventually got the breakthrough in the middle session when he had Chandrasinghe caught at slip with a fast-rising ball.
And while Thornton also removed Tom Rogers shortly after, it was always Pope who looked the most likely to take charge of the game.
He had Peter Handscomb superbly caught by man-of-the-match Ben Manenti at first slip for eight, then drew Sam Harper's back foot out of his crease to have him stumped for five.
And after Mitchell Perry chewed up 80 balls in a 25-over partnership with Kellaway, it was Pope who got the crucial wicket in the final hour.
The 24-year-old spun a ball back from outside the left-hander's off stump, bowling Perry for nine as the No.8 went back to cut.
Kellaway's wicket came in Pope's next over, before he had Peter Siddle caught at slip to leave Victoria nine wickets down.
And when No.11 McClure offered no shot to a ball that went straight on, Pope had ensured South Australia would stay second on the ladder with a rare win over their old rivals.
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