Australia captain Smith made 119 and opening batsman Marsh fell for 130 as the touring side went to tea on 316 for four. Adam Voges (22) and Mitchell Marsh (17) were unbeaten at the interval.
Sri Lanka, 2-0 up in the series, recovered from 26-5 to post a first innings total of 355 and still lead the world's top-ranked side by 39 runs.
Resuming on 141-1, Smith and Marsh kept the hosts wicketless through the morning session but both fell in the space of three overs after the new ball was taken after lunch.
The pair added 246 for the second wicket.
Marsh, playing his 18th test after a seven-month absence, was the first to get to his hundred, his fourth in tests, with a paddle sweep off Dilruwan Perera that went to the boundary.
The 33-year-old, replacing opener Joe Burns in this match, was dropped on 64 and 121. He was finally out when he chopped seamer Suranga Lakmal on to his stumps.
Smith used his feet brilliantly against the spinners and brought up his 15th test hundred with an on-driven single off Perera.
The right-hander was stumped smartly by wicketkeeper Kusal Perera off Rangana Herath who also dismissed all-rounder Moises Henriques (four) in similar fashion.