Jayawardene (224 not out) and vice-captain Kumar Sangakkara (229 not out) batted through the day on Friday to pile up a 471-run partnership, the second highest stand in the game's history.
Sri Lanka, who will resume on 485-2, have a 316 run first-innings lead with three days to play.
"We haven't thought about how long we are going to bat yet but we want to have a decent rest tonight and then make sure we continue to do the work tomorrow morning that we did today," Jayawardene told reporters.
"It is not finished yet and we want to make sure they stay down," he added.
"The longer we can bat the more the pitch will deteriorate and then hopefully our spinners can get plenty out of the surface in the last couple of days."
South Africa wicketkeeper Mark Boucher said the tourists were licking their wounds but would fight on.
"The guys are pretty down in the dressing room - it was just one of those days in Test cricket," Boucher said.
"It was very frustrating to go through a day's play without a single success, but a lot of cricketers have been through that in Test cricket and there is nothing much to do if you have given 100 percent," he added.
"There is no doubt that we are now up against it but trust me: if we go down, we'll go down fighting.
"The conditions are different here and a couple of us are off the ball but anything is possible in cricket," he said.
