After teammate Jake Lehmann also hit a ton, Scott plundered 147 as the home side surged to 426 and a first-innings lead of 231 at Adelaide Oval.
The Tigers then went to stumps at 3-73 in reply, still trailing by 158 runs at the end of day two after being all out for 195 on Friday.
A win would be vital for South Australia, who entered this round in fourth spot on the ladder, just behind Tasmania.
And their dominance was best summed up by Scott's innings, with the bowling allrounder having shown talent with the bat since his debut in 2019-20.
The 24-year-old fired from the moment he arrived at the crease, attacking Billy Stanlake and cutting him for five separate boundaries.
He also took to the spinners, bringing up his century and pumping the air in joy after one of two slog-sweeps that went for six off debutant Ruwantha Kellapotha.
Another six came when he used his feet and hit Nivethan Radhakrishnan back down the ground, before he later took Jackson Bird and Gabe Bell over the legside boundary.
Scott's innings came with Llyod Pope (36) offering support in a 76-run ninth-wicket stand that completely took the game away from the Tigers.
It came after Lehmann reached his second century of the summer, continuing on a late-career resurgence that began at the end of last season.
He reached 100 from 96 deliveries, before being bowled next ball when chopping onto his own stumps off Brad Hope.
After being put to the sword in the field Tasmania then slumped to 3-42 early in their second innings, with Jordan Buckingham (2-12) removing both Radhakrishnan and Hope.
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