When play was called off for the day because of rain and bad light, Thilan Samaraweera was unbeaten on 53 with wicketkeeper Romesh Kaluwitharana not out 30.
Atapattu reached his 15th Test century in the morning session on Sunday but failed to add to his score after lunch.
The 33-year-old right-hander was dismissed in the first over of the afternoon session for 133, caught at gully by Matthew Hayden off the pace bowling of Glenn McGrath.
Atapattu, who hit 19 fours and batted for five-and-a-half hours, had put on 124 for the third wicket with Mahela Jayawardene on a good batting wicket.
Jayawardene fell in the next over for 43, miscuing an attempted hook shot off Michael Kasprowicz to be caught by the bowler with the score on 280.
Australia had claimed two wickets for no runs but Samaraweera and Tillakaratne Dilshan guided Sri Lanka safely past the follow-on mark of 318 in a fifth-wicket stand of 65.
Australia leg spinner Shane Warne picked up his second wicket of the innings, finishing with figures of 2-117, and needs another five to equal Sri Lankan Muttiah Muralitharan's world record of 527.
WARNE STRIKES
Sri Lanka had resumed on their overnight score of 184 for two, with Atapattu on 75 and Jayawardene on nine.
Dilshan fell to Warne for 35 shortly after tea, leaving Sri Lanka on 345 for five. Samaraweera, however, resisted the Australia attack for three hours before the premature close, hitting five fours.
Kaluwitharana was hit on the crest of the helmet by a Jason Gillespie bouncer but continued to play his shots, hammering two boundaries in his 39-ball innings.
The touring side had added 96 runs without loss from 30 overs in the first session to reach lunch on 280 for two.
Atapattu reached his century with a boundary through the covers off the bowling off Gillespie 50 minutes into the day's play.
His hundred came in 265 minutes from 208 balls with 16 fours.
Kumar Sangakkara and Atapattu shared a second-wicket stand of 138 on Saturday before Warne had Sangakkara caught at long on for 74.
Justin Langer top-scored for Australia with 162, putting on 255 for the first wicket with Matthew Hayden (117), while Damien Martyn made 97.
Leg spinner Upul Chandana took 5-109 for Sri Lanka and young paceman Lasith Malinga claimed 4-149 as Australia lost their last seven wickets for 63 runs.
Australia lead the two-match series 1-0.
