The pace bowling duo of Gerard Denton and Damien Wright on Tuesday grabbed two wickets apiece in the final session of play to have South Australia reeling at 110 for four in its second innings - still needing 430 runs to win.
Tasmania, with a first innings lead of 95, had earlier scored 334 in its second innings with wicketkeeper Sean Clingeleffer top-scoring with 74.
Wright and Denton then further increased Tasmania's chances of an outright win when they each took an early second innings wicket, including that of former Australian Test player Greg Blewett for one, to have South Australia at 15 for two in the 10th over.
Young South Australian batsman Mark Cosgrove provided the only major counterpunch with a hard-hitting innings of 54 from 68 balls, which included nine boundaries.
He shared a 76-run stand with opener David Fitzgerald (26), before Denton returned to have Fitzgerald caught at slip late in the session, with Denton's yorking of Blewett, for one, also a major blow.
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