Duminy scored 100 not out as South Africa declared on 455-9 on the second day in Galle, with Sri Lanka closing on 30 without loss.
South Africa's total is the second highest they have achieved on Sri Lankan soil.
Middle-order batsman Duminy was ably assisted by all-rounder Vernon Philander (27) and tailender Morne Morkel (22).
And, although he was pleased with his efforts, Duminy is aware of the importance of putting Sri Lanka under immediate pressure on day three.
"I wasn't really thinking about the century until I got into my 80s," he said. "But, yes, it's always pleasing to get to triple figures in these conditions.
"The biggest challenge was the spinners and trying to marshal partnerships with the tailenders, especially Morkel.
"There is still plenty of hard work to be done. Friday is going to be crucial in setting up the game for us. Hopefully, we can make some early inroads."