South Australia scored 93 runs with Elliott taking 6 wickets for 23 runs, and were bowled out for 24 runs in their second innings, giving Tasmania a lead of 16 runs. Tasmania scored 101 runs with Doggett taking 6 wickets for 40 runs.
Paceman Brendan Doggett sparked a stunning South Australian comeback against Tasmania as 20 wickets tumbled on day one of their Sheffield Shield clash.
Shield leaders SA were skittled for 98 at Adelaide Oval on Tuesday with Tasmanian quick Kieran Elliott bagging a career-best six wicket haul.
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Doggett then shredded Tasmania, taking 6 for 40 as the visitors crashed to 101 all out. He captured five of the initial six Tasmania 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.
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 batters perished in identical fashion before the end of the fourth over with Tim Ward and Jordan Silk also caught behind off a rampant Doggett.
Kieran Elliott continued his stunning form with six wickets
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Liam Scott 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 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 for 23, the best return in first-class cricket for the Victorian born 29-year-old, to follow his 10-wicket match haul against Victoria in the previous round.
SA lost 7 for 17 in the middle session and only three batters reached double-figures - Jason Sangha, Conor McInerney and captain Nathan McSweeney.