Shaun Marsh and captain Steve Smith led Australia's revival with a partnership of impressive patience after Sri Lanka had built a healthy 355 all out on day two of the third Test.
Recalled opener Marsh and Smith combined for 120 runs on Sunday - David Warner the only man to fall for the tourists after making an eye-catching, yet underwhelming 11 as Australia closed the day on 141-1.
Earlier in Colombo, Dinesh Chandimal (132) posted his seventh Test hundred to take his innings-saving union with Dhananjaya de Silva to 211 before the latter fell for 129.
Smith ended the day on 61, having become just the second Australian to score a fifty in the series, with Marsh joining him in the following over and ending the day on 64.
Chandimal and De Silva had displayed Sri Lanka's desire for a series whitewash remained strong when rescuing their side from 26-5 on day one, but the latter fell to a persistent Nathan Lyon (3-110), who hung outside off stump long enough to find an edge and end the pair's 87-over resistance.
A dicey Chandimal almost threw his wicket away twice in the following over to Jon Holland, who soon after got his first wicket of the tour as Dilruwan Perera (16) miscued to extra cover, but Rangana Herath and Chandimal continued to take the game further away from Australia.
The pair had put 73 runs on before Herath was forced to retire hurt when a Mitchell Starc (5-63) delivery caught him sharply on the box.
Chandimal and Suranga Lakmal quickly fell to Starc, whose impressive return to the Test arena continued with a third five-for of the series.
Warner began the response by launching a first-ball Dilruwan full-toss over midwicket for six, but the left-hander was gone eight balls later, stumped attempting another expansive effort against the off-spinner.
Marsh was almost caught and run out off one Herath delivery after the veteran returned to the field and the opener was relieved to see two edges fall short of the slips.
There was a milestone for Smith as he drove Lakshan Sandakan for four to pass 4,000 Test runs with the captain and Marsh requiring continued fight on day three if Australia are to take anything from the series.