Green, Khawaja put Australia on top in Galle Test
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The tourists reached 313 for eight when bad light stopped play in Galle after storms and ferocious winds that collapsed a spectator stand and delayed the start of play until the afternoon.
Skipper Pat Cummins, on 26, and Nathan Lyon, on eight, were batting at close of play after the tourists dominated the two sessions.
The left-handed Khawaja made 71 before Green, who top-scored with 77, was involved in an attacking stand of 84 with wicketkeeper-batsman Alex Carey.
Ramesh Mendis soon removed Carey at 45 to break the stand and claimed his fourth wicket of the innings when he trapped Green lbw.
Mitchell Starc fell next to debutant leg-spinner Jeffrey Vandersay, who took two wickets, but Cummins smashed the bowlers around in his 16-ball blitz that included one four and three sixes.
The tourists, who resumed on 98-3, lost Travis Head on his overnight six with off-spinner Dhananjaya de Silva getting the left-hander caught and bowled.
Khawaja, a left-handed opener who survived a missed stumping on 36 during the previous day, added 57 in partnership with Green.
Vandersay finally dispatched Khawaja, who has been in top form after playing a key role in his team's 1-0 test triumph in Pakistan in March, for his maiden Test wicket.
The left-handed Carey joined Green and took the attack to the opposition as he used the sweep to good effect and hit six boundaries.
Ferocious Indian Ocean winds battered Galle on Thursday, upending broadcast equipment and one of the sightscreens at the ground in the port city.
The makeshift roof of one of the ground's smaller stands was also brought down by the storm. No injuries were reported.
Once the rain stopped, ground staff worked quickly to set things in order and get the game underway.
Lyon led the Australian charge at the start of the two-match series with his 20th Test five-wicket haul, which helped bowl out Sri Lanka in the final session of play.
Sri Lanka 1st innings (212 all out; N. Dickwella 58, N. Lyon 5-90, Swepson 3-55)
Australia 1st innings (overnight 98-3, Khawaja 47, Head 6)
U. Khawaja c Nissanka b Vandersay 71
D. Warner lbw b R. Mendis 25
M. Labuschagne c Fernando b R. Mendis 13
S. Smith run out (Dickwella/K. Mendis) 6
T. Head c and b De Silva 6
C. Green lbw b R. Mendis 77
A. Carey c Chandimal b R. Mendis 45
M. Starc c and b Vandersay 10
P. Cummins not out 26
N. Lyon not out 8
Extras (b20, lb3, nb1, w2) 26
Total (8 wickets, 69 overs) 313