Dimuth Karunaratne and Lahiru Thirimanne were both unbeaten on eight, weathering some 30 minutes before bad light stopped play slightly early.
At stumps, Sri Lanka were 123 for three in reply to Australia's 534-5d
The 21-year-old was overlooked for the first Test in Brisbane and again missed out on selection for the second Test currently being played in Canberra
On a cool, overcast day, Burns and Head dug Australia out of a hole after they lost Marcus Harris, Usman Khawaja and Marnus Labuschagne cheaply
On the back of the Brisbane thumping, Australia have opted to go with an unchanged side for the second Test in Canberra
Hathurusingha was officially removed from the on-tour selection panel, governing body Sri Lanka Cricket (SLC) said
'Mitch has got all of my support and everyone's support in that change room, so it is pretty unfair criticism in my eyes'
In another injury blow, Sri Lanka Cricket said Dushmantha Chameera had been ruled out of the final Test at Canberra.
Sri Lanka 144 in the first innings and just 139 in the second in reply to Australia's first innings total of 323.
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