Duminy (100 not out) hit 10 fours in his impressive knock to guide South Africa to their second highest total on Sri Lankan soil as the visitors declared on 455-9 on day two in Galle.
Wicketkeeper Quinton de Kock (51) reached his first Test 50 in only his second outing in the five-day format, while Vernon Philander (27) and Morne Morkel (22) also made valuable contributions down the order.
It was a day of toil for the Sri Lanka attack who, minus the talents of pace bowler Shaminda Eranga - sidelined with a hand injury sustained while fielding on the first day - struggled on a largely lifeless pitch.
The hosts were able to mount a solid start to their reply before the close of play, Upul Tharanga (20 not out) showing aggression with the bat as Sri Lanka finished on 30-0.
Having reduced South Africa to 268-5 at the end of the first day, Sri Lanka will have been hopeful of restricting Hashim Amla's men to a relatively small total.
But, although Dale Steyn (3) was soon bowled by Suranga Lakmal (3-75), De Kock did his best to temper those expectations by scoring his maiden half-century.
Any prospect of a promising partnership between De Kock and Duminy was ended just four balls after that milestone, though, as the former edged a wonderful turning delivery from Dilruwan Perera (4-162) into the hands of Mahela Jayawardene.
Yet Sri Lanka were frustrated by the tail, Duminy displaying superb resistance to put on stands of 75 and 66 with Philander and Morkel respectively.
Duminy capped off a composed display with a sweep for a single to mark the second hundred of the South Africa innings - and only his fourth in Tests - following Dean Elgar's effort on the first day.
Morkel was dismissed by Perera with the very next ball, bringing about South Africa's declaration but - after Tharanga's early show of intent - Sri Lanka should be confident of mounting a competitive response.