Jayasuriya bags six as Sri Lanka bowl out Australia for 364
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Sri Lanka were eight for no loss at lunch with Pathum Nissanka, on three, and skipper Dimuth Karunaratne, on five, surviving three overs of pace from Mitchell Starc and Pat Cummins.
The tourists resumed on 298-5 with Smith and Alex Carey taking their sixth-wicket stand to 77 before Jayasuriya broke through with the score on 329.
Jayasuriya, who took three wickets on the opening day, set a trap for Carey who miscued a reverse sweep to be caught at backward point for 28.
The left-arm spinner soon got Mitchell Starc out for one to become the seventh Sri Lankan bowler to take five wickets in an innings on Test debut.
Fast bowler Kasun Rajitha and 'mystery' spinner Maheesh Theekshana also struck as Smith ran out of partners.
Smith and Marnus Labuschagne led Australia's dominance on day one with a third-wicket partnership of 134 as the pair took the attack to the opposition bowlers.
Labuschagne hit his first overseas century as he made 104 before being stumped off Jayasuriya.
Smith ended his century drought of 18 months to notch up his 28th Test ton, ending the first day on 109.
The second day's play in the port city had few spectators, with hundreds of protesters demanding the resignation of President Gotabaya Rajapaksa outside the ground.
Sri Lanka is enduring its worst ever economic crisis and much of the public has accused Rajapaksa's government of chronic mismanagement.
Australia 1st innings (overnight 298-5, Smith 109, Carey 16)
U. Khawaja b R. Mendis 37
D. Warner b Rajitha 5
M. Labuschagne st Dickwella b Jayasuriya 104
S. Smith not out 145
T. Head b Jayasuriya 12
C. Green lbw b Jayasuriya 4
A. Carey c R. Mendis b Jayasuriya 28
M. Starc c K. Mendis b Jayasuriya 1
P. Cummins lbw b Rajitha 5
N. Lyon lbw b Jayasuriya 5
M. Swepson Swepson lbw b Theekshana 3
Extras (b5, lb6, w1, nb3) 15
Total (all out, 110 overs) 364
Fall of wickets: 1-15 (Warner), 2-70 (Khawaja), 3-204 (Marnus Labuschagne), 4-238 (Head), 5-252 (Green), 6-329 (Carey), 7-333 (Starc), 8-338 (Cummins), 9-345 (Lyon), 10-364 (Swepson)
Bowling: Rajitha 25-4-70-2 (w1, nb3), R. Mendis 33-1-117-1, Theekshana 16-2-48-1, Jayasuriya 36-3-118-6
Umpires: Kumar Dharmasena (SRI), Michael Gough (ENG)
TV umpire: Nitin Menon (IND)
Match referee: Javagal Srinath (IND)