Sri Lanka, seeking a series-levelling win, closed the second day at 166-2 in their first innings after a batting masterclass from Michael Hussey had steered the tourists out of trouble at the Sinhalese Sports Club.
Mahela Jayawardene chipped in with 31 not out in a third-wicket stand of 69 with Sangakkara to leave the hosts 150 runs behind with eight wickets in hand.
Hussey followed a match-winning 95 in the first Test in Galle and 142 in the drawn second game at Pallekele with a fluent 118 studded with 12 boundaries and two sixes.
The left-hander, a veteran of 62 Tests, passed 5,000 Test runs on the way to his 15th century -- the fourth against Sri Lanka.
The 36-year-old's value to the team can be gauged by the fact that he has scored four of Australia's last six Test centuries, the other two coming from the blades of Brad Haddin and Shaun Marsh.
The hosts began their reply slowly as the left-handed opening pair of Tharanga Paranavitana and Lahiru Thirimanne took 25 overs to put