Former captains Sangakkara (69 not out) and Jayawardene (38 not out) looked well settled too, having starred in an unbroken 95-run third wicket stand when bad light stopped the fourth day's play with the hosts on 223 for two.
Australia captain Michael Clarke had declared their first innings at 411 for seven before the start of the day's play, giving his bowlers as much time as possible to bowl out the hosts for a second time in the rain-hit match.
This is Sri Lanka's best batting performance in the series, aided by a patient 158-ball knock from Sangakkara who scored his 35th test half-century in his 99th test appearance in his home district of Kandy.
"I think it's important we show some characters in this innings, especially since the last three innings we had opportunities to really try and win test matches but we haven't done a bit of batting," Sangakkara told reporters.
The left-handed batsman, along with Jayawardene, frustrated the Australian bowlers who removed openers Tharanga Paranavitana (55) and Sri Lanka skipper Tillakaratne Dilshan (36) but did not get another chance to celebrate.
Sangakkara said Sri Lanka's job, having folded for 174 in the first innings, was far from over.
"Test matches are usually won or lost on the first innings. Very rarely you see huge comeback in the third and fourth innings. So, as a batting side, going against Australia, we got to be up for the fight," he said.
"If we get a good start tomorrow morning, because the new ball is due in one over, we can put pressure back on the Australians."
Sri Lanka's misfiring openers stitched together an 81-run stand, their best in the series, before captain Dilshan was caught by Shane Watson off Ryan Harris for 36 in the morning session.
After lunch, Australia's part-time bowler Michael Hussey removed Paranavitana with the fifth ball of his first over, to add to his first innings scalp of Sangakkara.
Umpire Tony Hill had to change his 'not out' decision as Australia captain Michael Clarke asked for a review on stumper Brad Haddin's strong request, even though Hussey did not even appeal.
"There was a good noise. I was pretty confident it had nicked the glove," Haddin told reporters.
Paranavitana could not carry on but his 143-ball knock helped steady the home team, who had lost the first five wickets before reaching 80 in the first innings.
Australia won the first test of the three-match series in Galle by 125 runs.
