Shield leaders SA were skittled for 98 at Adelaide Oval on Tuesday with Tasmanian quick Kieran Elliott bagging a career-best six wicket haul.
Doggett then shredded Tasmania, taking 6-40 as the visitors crashed to 101 all out.
SA were 0-24 in their second innings at stumps.
Doggett captured five of the initial six Tasmanian wickets on a pitch offering considerable movement off the seam.
Just three Tasmanians reached double-figures with new Test allrounder Beau Webster top-scoring with 28, Jake Doran making 18 and Aidan O'Connor 14.
Doggett started his spree by dismissing former SA opener Jake Weatherald for a golden duck when the left-hander edged to wicketkeeper Harry Nielsen.
Two more batsmen perished in identical fashion before the end of the fourth over with Tim Ward (four) and Jordan Silk (duck) also caught behind off a rampant Doggett.
Liam Scott (1-12) chipped in with the wicket of Doran - the left-hander pulled a short delivery to midwicket where Lloyd Pope plucked a screamer of a one-handed catch.
Doggett then returned to take another two consecutive wickets including Hobart Hurricances' BBL hero Mitchell Owen for a second-ball duck.
Webster launched a counter-attack before legspinner Pope (2-18) helped clean up the tail and ensure opening-day honours were shared.
Earlier, SA's batsmen collapsed amid precision seam bowling from Elliott and Gabe Bell.
Elliott took 6-23, the best return in first-class cricket for the Victorian born 29-year-old, and Bell claimed 3-21.
SA lost 7-17 in the middle session and only three batsmen reached double-figures - Jason Sangha (28), Conor McInerney (22) and captain Nathan McSweeney (20).
18°C