Hobart Test: Australia 8 wickets from Test win over Sri Lanka
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"If we can bat through tomorrow's first session without losing a wicket, it's going to be a good game. It's just an up-and-down track, a good track. It's going to be an interesting day," Herath said.
Australia had collapsed, losing the last eight wickets in their second innings for 146 after openers David Warner (68) and Ed Cowan (56) put on 132.
Left-arm spinner Herath captured five for 95 to lead the tourists' counter-attack and now has 60 wickets for the calendar year.
The home side had gone to lunch on a still-comfortable 146 for two before their innings unravelled in the middle session as they chased quick runs.
Shane Watson was out three overs after lunch, losing a stumping referral off Herath for five. He was soon followed by Phil Hughes, who chopped Shaminda Eranga onto his stumps for 16.
Matthew Wade, up the order, hit 11 before he holed out to Nuwan Kulasekara at long on off Herath.
Clarke went after the runs and reached his fastest Test half-century off 43 balls, but then called for the team physio and retired hurt.
The wickets kept tumbling and Peter Siddle was brilliantly snapped up by a diving Prasanna Jayawardene off Chanaka Welegedara for four.
Starc hit five before he was leg before wicket to Welegedara and the last able-bodied Australian player Nathan Lyon added 11.
Hilfenhaus, inconvenienced by a side strain, lasted eight balls before he became Herath's fifth wicket when lbw for a duck.
The afternoon clatter of wickets was in sharp contrast to the extended morning session when Warner and Cowan were largely untroubled.
Warner turned on the fireworks to slog Herath for six over long-on and then cheekily switch-hit the left-arm spinner for four.
But in attempting to cut Herath he feathered a catch to wicketkeeper Jayawardene on 68. Cowan was bowled off-stump by Welegedara for 56 with one that cut back in.