Sri Lanka imploded under blue skies before going to lunch on Saturday at 3-75 in their second innings, still 414 runs behind Australia's mammoth total of 6-654 declared.
In total, the hosts lost eight wickets either side of the follow-on playing on a dusty pitch that will only become more difficult to bat on.
Newly fit offspinner Matthew Kuhnemann (5-63) posted the second "five-fer" of his four-match Test career, helping Australia skittle Sri Lanka inside 45 minutes on day four.
Travis Head (left) congratulates Matthew Kuhnemann on one of his five wickets. (AP PHOTO)
Only two and a half weeks ago the left-armer's hopes of touring had been rocked when he dislocated his right thumb playing in the Big Bash League.
Sri Lanka started Saturday at 5-136 in their first innings but lost 5-9 in 26 balls and were all out for 165, only former captain Dinesh Chandimal (72) challenging Australia's all-star bowling cartel.
Opening the bowling in the second innings, Mitch Starc (1-11) and Todd Murphy (1-33) dispatched of both openers as Sri Lanka fell to 2-6.
Starc was at his brutal best with the new ball, striking Oshada Fernando (6) lbw before the back-up opener lodged one of the all-time worst reviews.
Mitch Starc (right) shone with the new ball, taking the early wicket of Oshada Fernando. (AP PHOTO)
Ball Tracker showed a near unplayable Starc in-swinger would have contacted the 32-year-old's middle stump.
After a wicketless first innings, Murphy embarrassed opener Dimuth Karunaratne (0), who left him alone only to find his off stump rattled.
On the last ball before lunch, Australia reviewed to claim the big wicket of Chandimal for the second time in the session.
The former captain gloved Nathan Lyon (1-17) to Travis Head at short leg as Australia broke a 69-run partnership between he and Angelo Mathews (34no).
Tropical Galle weather could be the biggest obstacle to Australia's hopes of winning inside four days. Rain is forecast for the afternoon after Friday's last two sessions were washed out.
The last time Australia won by more than an innings was in the series opener of the 2022 tour of Sri Lanka.
Earlier, Kuhnemann and Lyon (3-57) skittled Sri Lanka's last recognised batters inside half an hour en route to a 489-run first-innings lead.
Australian spinner Nathan Lyon took Dinesh Chandimal's wicket twice in a session. (AP PHOTO)
It marked Australia's biggest first-innings advantage since 2003, when opener Matthew Hayden scored a then world-record 380 runs against Zimbabwe in Perth.
Kuhnemann called Steve Smith a tactical "genius" after day three and would have felt the same way when Kusal Mendis (21) fell right into the captain's trap early on day four.
The wicketkeeper's sweep ballooned up to Murphy, who had been placed at square leg for exactly that kind of a shot.
With his diving catch on Mendis, Murphy helped Australia open the floodgates and cut into Sri Lanka's bowlers in a wicket maiden for Kuhnemann.
In the next over, Lyon took the prized wicket of Chandimal, who fell attempting the sweep shot that worked so well for Australia in their best-ever subcontinent innings.
Bowling around the wicket, Lyon struck Chandimal's back pad and Ball Tracker showed the delivery striking off stump after the former captain unsuccessfully reviewed.
The Sri Lankan tail could not wag, with Alex Carey stumping Prabath Jayasuriya (0) from Kuhnemann's bowling.
It was the mild-mannered Kuhnemann who finished the innings when Jeffrey Vandersay (4) skied him to Starc at cover.
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