Paceman Copeland removed opener Tillakaratne Dilshan (4) with the second ball of his test career after the home captain had smashed a boundary off his first, while right arm spinner Lyon dismissed Kumar Sangakkara with his debut delivery.
At lunch, Sri Lanka were struggling on 54 for three wickets in reply to Australia's first innings total of 273.
Dilshan was hoping to give Copeland a rude introduction to the test arena with a show of aggression when the 25-year-old was asked to bowl the second over, but after his initial blast, the Sri Lankan gave up a smart catch to Ricky Ponting at cover.
A subdued Sangakkara then batted for an hour to score 10 runs from 40 balls before being caught by Australian captain Michael Clarke with an excellent low catch at slip off Lyon's first ball in the 16th over of the innings.
Mahela Jayawardene, who joined opener Tharanga Paranavitana for the third wicket, tried to accelerate the pedestrian run rate but was run out for 11 by Copeland as he attempted an unnecessary single, leaving the hosts in trouble at 44-3.
At the interval, Paranavitana was unbeaten on a grinding 17 from 85 balls as the hosts scored at less than two runs per over on a slow pitch that favours the spin bowlers.
On Wednesday, Michael Hussey scored a steady and patient 95 to lift Australia to a competitive total which Sri Lanka, still 219 runs in arrears, will do well to match.
The tourists beat Sri Lanka 3-2 in the one-dayers ahead of the three-match test series.
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