Australia will take a 41-run led into the fourth day after finishing Sunday's play at 180 for five wickets.
Khawaja and Mitchell Marsh put on 87 runs for the fifth wicket before Khawaja, whose place in the team has been under threat, was trapped leg before wicket by Kagiso Rabada in the second last over of the day.
"We didn't ask enough questions around the off stump for a while but once we did again, we got the reward," said South Africa's AB de Villiers after the close.
The tourists had been teetering at 86-4 just after tea, when Khawaja was joined by Marsh, who played a solid supporting role to end the day on 39 not out. He will resume on Monday with Tim Paine, who has five runs to his name.
Australia lost three wickets in the second session after lunch, including that of captain Steve Smith, and then Shaun Marsh with the second ball of the last session.
Smith, ranked the world's top test batsmen, went cheaply as he was caught behind for 11 off the spin bowling of Keshav Maharaj while David Warner, also a key player, was bowled by Rabada for 13.
South Africa had a first innings lead of 139 after being bowled out for 382 just before lunch. De Villiers notched up his 22nd test century in scoring an unbeaten 126 in a busy morning session.
He had not scored a ton in his last 13 tests but featured in an 84-run partnership with Vernon Philander (36) for the eighth wicket and a further 58 with Keshav Maharaj, who swatted at the Australian bowling to score 30 off 24 balls.
"We are in a decent position and our bowlers will certainly come out with a lot of fire in the morning," de Villiers said. "We will be confident chasing 150 but not much more."
Australia lead the four-test series 1-0.
(Reporting by Mark Gleeson; Editing by Amlan Chakraborty, Pritha Sarkar and John Stonestreet)
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