Australia skipper Pat Cummins said Nathan Lyon's nine wickets "showed his class" in the team's Friday thrashing of Sri Lanka in the opening Test.

Lyon bamboozled the opposition batsmen with his off-spin in a match that ended before lunch on day three in Galle, with the hosts bowled out for 212 and 113.

The champion off-spinner pushed past former Indian fast bowler Kapil Dev's 434 wicket tally in the morning to break into the top-10 ranking of all-time Test bowlers.

"Nathan Lyon showed his class, he looked unplayable out there and built off the back of a really good batting day," Cummins told reporters after play wrapped up.

Lyon, 34, led the charge with his five-wicket haul in the first innings and then took four on the third morning to flatten the Sri Lankan batting in their own den.

He was ably supported by Mitchell Swepson, a leg-spinner, and occasional spinner Travis Head who got his maiden Test wicket and then took three more.

"He's unplayable for left or right handers," Cummins said of Lyon, who has now made 436 wickets across 109 Test matches.

"Sometimes out here, bounce of spinners is spoken about as something that's not desirable, but he showed here with that bounce he was unplayable," he added.

'Fast learner'

Batsman Cameron Green was named man of the match in a bowler-dominated Test, handling Sri Lanka's spin roster with confidence for a first innings showing of 77.

Cummins said his younger batters like the 23-year-old Green had played in sub-continent conditions before, but that had given little preparation for the turn on Galle's notoriously tricky wicket.

"I think we had Marnus (Labuschagne), Travis Head, Cameron Green, Alex Carey (but they) hadn't played Test matches in conditions that have spun this much," said Cummins.

"We have a big series next year in India, so this can only help develop and fast-track our batters," he added. "Absolutely you learn so much from these tours."

Green had always been a "fast learner", Cummins said.

"But it's even surprised us how fast he's learnt out there. From ball one, really sharp (with) a really clear method."

Australia were five down for 157 when opener Usman Khawaja departed on day two.

Green put on an 84-run stand with Carey to put the team on course to its 109-run lead at the end of the innings.

The second and final Test begins July 8 at the same venue.