Buoyed by 142 from Mike Hussey and 141 from Shaun Marsh on his debut, the tourists were 411-7 when rain stopped play soon after lunch. Usman Khawaja was batting on 13 with tailender Ryan Harris on nine. Australia still had a healthy 237-run lead.
"Very surreal at the moment, very proud day," Marsh said about his century on debut. "Still can't believe really to be playing Test cricket, to be given an opportunity to get here and get a hundred in my first innings."
"I was enjoying every minute of it," he said of the seven hours he spent at the crease.
Marsh's father, Geoff, was an Australian test opener in the 1980s and early 1990s before becoming Australia coach, a national selector and, most recently, coach of Zimbabwe.
"He was very happy I could see, very emotional for him," Marsh said of his father, who presented him with his baggy green international cap and watched him play from the stands.
Australia was 378 for four at lunch but lost the wickets of Marsh, Brad Haddin and Mitchell Johnson during the eight overs of play that were possible afterward.
Marsh was caught by Kumar Sangakkara off seamer Suranga Lakmal, failing to keep down a rising delivery with his pull shot and Sangakkara diving forward to take the catch at deep square-leg. He had spent seven hours at the crease, faced 315 balls and hit 18 boundaries.
Randiv came to bowl the 129th over and dismissed Haddin with his second ball, having him caught by Sangakkara at mid-on. He delivered an arm ball next at Johnson who left it and was bowled.
The wickets came as a relief for the hosts whose bowlers toiled for over five hours without a wicket during a 258-run partnership between Hussey and Marsh — the best fourth wicket partnership in tests between the two nations.
Marsh, who started the day on 87, reached his maiden test century three deliveries after Hussey, sweeping offspinner Randiv for two runs. Hussey faced 244 balls and hit 16 boundaries before being dismissed in the morning session caught by Sangakkara off spinner Thilan Samaraweera.
Randiv had the best bowling figures for Sri Lanka 3-103 while Lakmal returned 2-102.
Sri Lanka was dismissed for 174 in its first innings but the team's coach Rumesh Ratnayake said he was still positive that Sri Lanka could turn it around despite the disappointing batting.
"I would think everybody is aware what we have to do. If you saw the way the Aussies did it, it was a placid track from day one, we did not capitalize on that," he said.
"As a coach I am confident, that is what I would build up in the team," Ratnayake added. "I have no doubt the talent we have, as you all know, is capable of big scores."
