Duminy hit 100 not out in 206 balls to enable South Africa to declare on 455 for nine before Sri Lanka closed on 30 without loss in reply.
Duminy, whose fourth Test century included 10 boundaries, says that he expects the game to move along quickly on the final two days so the middle day is vitally important.
"It's going to be a lot of hard work," Duminy said.
"The wicket is pretty flat for the seamers, but there is a little bit there for the spinners.
"The game will probably speed up on day four and five so tomorrow is going to be a crucial day to set up those last two days."
Duminy had to work hard to build half-century partnerships with Vernon Philander (27) and Morne Morkel (22) to put South Africa in a strong position.
"The biggest challenge was the spinners," he said.
"Trying to marshal the partnership as best as possible, especially with Morne.
"Vernon and I have played together a long time so we sort of understand each other's games.
"Marshalling that partnership with Morne was crucial, and to see how he applied himself today was exceptional."
Duminy's century came with him batting at number seven and he said he was pleased to have reached three figures.
"It's always pleasing to get to three figures in these conditions," he said.
"I think understanding my role within the team is more crucial. Batting at seven and trying to marshal the lower order as best a possible has always been key for me.
"The hundred will come if I bat as long as possible, so I'm pretty pleased with getting the ton here today.
"There is still a lot of hard to be done, there might still be an opportunity for a job with the ball so there are still three big days to come."
© Cricket World 2014