Pushing to avoid a series whitewash, Sri Lanka undid their good work from the first session as they lost 4-34 on a pitch tipped to only become trickier for the batters.
There's plenty of turn in the wicket already, with Dinesh Chandimal (70no) the batting order's shining light for a second-straight Test.
Sri Lanka went to tea at 5-144 after eating their lunch on 1-87.
Only one wicket away from 550 Test scalps, Lyon (3-42) needed only 10 minutes to swing momentum in Australia's favour after lunch.
He bowled around the wicket and snuck past the bat of retiring opener Dimuth Karunaratne (36) to break a 70-run stand with Chandimal.
Fellow veteran Angelo Mathews (1 off 26 balls) never looked comfortable replacing Karunaratne and walked immediately after edging Lyon to Alex Carey.
Within an hour of lunch, Lyon could have become the seventh man to reach 550 Test wickets but Kamindu Mendis successfully reviewed what the umpire thought was an edge.
But Sri Lanka's best batter of 2024 Kamindu Mendis was no match for Head's part-time off-spin.
Only two days ago, Head (1-18) could not bring himself to remove his sunglasses to front the press the morning after celebrating his Allan Border Medal win.
But he was back in peak condition during the second session, at the same ground where he took career-best figures on Australia's 2022 tour.
After Kamindu (13) edged him to Steve Smith in the slips, Head whipped his right wrist around to signify his "hot hand".
Australia's sole front-line quick Mitchell Starc (1-18) found plenty of reverse swing in an imperious second session and continued a miserable series for Sri Lanka's captain.
With the toe of his bat, Dhananjaya De Silva whipped Starc straight to Beau Webster at gully on the first ball he faced, leaving Sri Lanka in all sorts at 5-127.
Earlier, Connolly earned a Test debut in only his fifth first-class match, becoming Australia's least experienced debutant since 2011, when Pat Cummins played a Test in his fourth.
Former Test player Simon Katich presented Connolly with his baggy green as front-line spinner Todd Murphy dropped out of the XI after having a middling series opener.
Before his first over with the ball, Connolly had a brief chat with Lyon, who memorably took Kumar Sangakarra's wicket with his first delivery as a Test cricketer at the same ground in 2011.
Left-arm off-spinner Connolly (0-3) looked comfortable in his first two overs as a Test cricketer just before lunch, sending down a maiden in his second.
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