Australia, who bowled Sri Lanka out for 174 on the opening day having easily won the first test, reached 264 for three at the close with Marsh, who replaced former captain Ricky Ponting in the side, on 87 having shared a 148-run unbroken fourth wicket stand with Michael Hussey, who was 76 not out.
Only 4.3 overs of play were possible in the third session before the match was stopped due to bad light.
"We've played all our cricket together for Western Australia," Michael Hussey said of Marsh.
"I remember he made 90 in his debut and I remember batting with him for quite a period of time in his first game and he had a very similar sort of tempo... he showed tremendous concentration," he said.
"There were some periods where the scoring was more difficult. They bowled really tight for a while and he showed great concentration.
"Obviously he would be a bit nervous overnight, but hopefully we can start well again in the morning." Resuming at 133 for three after lunch, Marsh scored patiently and slowly, playing a supporting role to his experienced partner Hussey.
"The wicket played a lot better today than it did early yesterday," Hussey said.
"There is certainly no real swing movement for the fast bowlers and even with the second new ball, I think the wicket played quite slow, quite flat for the fast bowlers. It wasn't taking a lot of spin either."
Sri Lanka's bowlers toiled and captain Tillakaratne Dilshan used seven bowlers including himself and part timers Kumar Sangakkara and Thilan Samaraweera without any success in the second session.
Fast bowler Suranga Lakmal and spinner Suraj Randiv dismissed both Australian openers in the morning session.
Australia had not added to their overnight 60-0 when Lakmal bowled Shane Watson (36) with his second ball of the day, which the batsman wrongly decided to leave.
Randiv then dismissed Phillip Hughes also for 36 when Tharanga Paranavitana jumped forward from short-leg to hold a bat-and-pad catch.
Australia captain Michael Clarke (13) was then well caught by Mahela Jayawardene at second slip off Chanaka Welegedara when the total was 116.
Australia won the first test of the three-match series in Galle by 125 runs.
