Australia had appeared on course for a big first innings lead after a 246-run partnership between centurions Steven Smith and Shaun Marsh, but the loss of both batsmen in quick succession dented their prospects.
Adam Voges was batting on 22 while Mitchell Marsh was on 17 at the break with the visitors still trailing the hosts by 39 runs in response to Sri Lanka's 355.
Marsh, who had hit his 19th boundary off the previous delivery, was bowled on 130 after he chopped Lakmal's good length delivery onto his stumps.
Smith, who hit 10 fours and a six during his 119-run knock, departed after being stumped off Herath with the third umpire ruling a close decision in favour of the bowler.
The marathon partnership between Smith and Marsh was the highest second-wicket stand between the two countries.
Marsh, who was drafted into the Australia side because of his long experience of Asian conditions, survived a dropped catch on 67 early in the morning against Herath but soon took control.
He brought up his hundred with an inside edge off Dilruwan Perera that went for a boundary and he celebrated the milestone by hugging his skipper at the other end.
Smith, who resumed the day on 61, reached his 15th Test century to improve on his previous best of 55 in the series.
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