Australia were 411 for seven when the day's play was called off after only eight overs were bowled in the second session. Usman Khawaja was batting on 13 and Ryan Harris batting on nine.
Marsh and Hussey extended their fourth-wicket partnership to 258 before Hussey was dismissed for 142, his 14th Test century.
The 28-year-old Marsh, who made 141, notched his hundred in front of his father and former Australian opener Geoff Marsh, who gave the traditional baggy green cap to his son.
SCORE BOARD
Sri Lanka (I innings) 174
Australia (I innings, O/n: 264-3):
Watson b Lakmal 36
Hughes c Paranavitana b Randiv 36
Marsh c Sangakkara b Lakmal 141
Clarke c M J’rdene b W’dara 13
M Hussey c S’kkara b S’weera 142
Khawaja (batting) 13
Haddin c Sangakkara b Randiv 1
Johnson b Randiv 0
Harris (batting) 9
Extras (LB-9, W-1, NB-10) 20
Total (for 7 wkts, 132 overs) 411
Fall of wickets: 1-60, 2-95, 3-116, 4-374, 5-391, 6-392, 7-392.
Bowling: Welegedara 23-3-74-1, Lakmal 23-2-102-2, Prasanna 23-3-80-0, Dilshan 14-4-32-0, Randiv 43-7-103-3, Sangakkara 2-0-4-0, Samaraweera 4-0-7-1.
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