Australia were precariously placed at 83 for three, with Smith unbeaten on 26, when bad light forced the umpires to call tea early on the fourth day in Pallekele in a match that has already been badly hit by rain.
Australia still need another 185 runs for victory to take a lead in the three-match series.
Rangana Herath struck early with his left-arm spin when the veteran bowled David Warner for one. Offspinner Dilruwan Perera then soon had Usman Khawaja trapped lbw with the score reading 33/2.
Smith then began a battling 54-ball innings, which has so far not seen him score any boundaries. His partner Adam Voges was similarly steadfast as the Australians looked to consolidate their status as the number one Test team.
Earlier it was Kusal Mendis' superb maiden century of 176 that helped Sri Lanka seize control of proceedings after lagging behind for three full days in a match shortened by several rain interruptions.