Mitchell Starc and Shane Watson took Sri Lanka's openers for just 65 to leave them chasing an unlikely 393 for victory in Hobart.
Sri Lanka face final day struggle in first Test against Australia
Sri Lanka's hopes are in the experienced hands of Kumar Sangakkara (18 not out) and skipper Mahela Jayawardene (five not out) after Tillakaratne Dilshan and Dimuth Karunaratne both fell victim to superb deliveries.
Australia skipper Michael Clarke had earlier played a glittering cameo by smashing 57 runs off 46 balls to help drive the hosts to 278 in their second innings before he retired hurt with a hamstring injury.
Sri Lanka were dismissed for 336 on Sunday in reply to Australia's first innings 450 for five declared and will need to set a new record for a fourth innings run chase at Hobart to beat the 369 Australia scored against Pakistan in 1999.
Spinner Rangana Herath took five for 95 and seamer Chanaka Welegedara 3-89 as the Sri Lankan bowlers finally got some reward for their efforts after the Australian openers frustrated them for much of the morning.
Their Australian counterparts made a more immediate effect as they looked to remove the last 10 wickets and take a 1-0 lead in the three-match series.
Shane Watson, taking on a bigger bowling burden after Sunday's injury to quick Ben Hilfenhaus, struck with his first ball to remove Dilshan, who made 147 in the first innings, caught behind for 11.
Karunaratne had put 30 runs on the board when he was undone by a sizzling Mitchell Starc yorker which hammered into the base of the off stump.
Jayawardene took 25 balls to get off the mark and Sangakkara had a big scare on three when Clarke, who had come out to field despite his injury, dropped the ICC cricketer of the year in the slips.
In the morning sunshine, openers David Warner (68) and Ed Cowan (56) combined for a partnership of 132 but both were removed in the half-hour before lunch in an appetiser for what was to come in the second session.
Herath had been belted for a six and a switch-hit four by Warner but got his revenge when his delivery took a bottom edge and carried to the wicketkeeper.
Cowan joined his partner in the pavilion 15 minutes later when Welegedara swung in a fizzing delivery which hit the Australian's pad before taking off the bails.
Watson suffered torrid examination from Herath before he was stumped by wicketkeeper Prasanna Jayawardene for five soon after lunch to bring Wade in at number five as they looked to up the run rate heading towards a declaration.
Three overs later, however, Phil Hughes played the ball onto his own wicket to depart for 16 and Wade did not last much longer, holing out to Kulasekara for 11.
After Clarke's departure, Peter Siddle (four), Starc (five) and Lyon (11) made brief appearances before Herath trapped Hilfenhaus lbw for a duck to end the innings and bring up tea.
The final wicket gave Herath 60 for 2012 to put him ahead of England's Graeme Swann in their personal battle to decide the most prolific wicket-taker of the year.
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