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Johannesburg: Sri Lanka lost four wickets on 80 in uphill response before bad light forced early stumps, need 147-run to avoid follow-on.
Kaushal Silva and Kusal Mendis survived the odd streaky moment to reach tea but both fell soon after to Rabada.
Another thin edge behind did for Silva to end a 47-run stand before Mendis, who struck six fours and a six and also saw the debutant Duanne Olivier put down a straightforward caught-and-bowled chance during a lively knock, was chiselled out by Rabada's bouncer, a simple catch lobbing off the gloves to gully.
In the next over, Dhananjaya de Silva speared a drive point as Sri Lanka subsided to 70 for 4.
On their best day of the series, Sri Lanka's bowlers claimed South Africa's seven remaining wickets for 88 runs.
Nuwan Pradeep took four wickets in as many overs to finish with four for 78, while Lahiru Kumara took four for 107.
Hashim Amla, who resumed on 125 not out, could add only nine more runs off 44 balls before he was caught behind to become Pradeep's third victim.
Although Pradeep was the most successful bowler, it was an impressive collective bowling performance by the Sri Lankan seamers in overcast conditions on a pitch which seemed to have more life than on the first day.
Suranga Lakmal bowled superbly from the start of play after South Africa resumed at 338 for three, conceding nine runs in seven overs, four of which came from overthrows, and having South African captain Faf du Plessis dropped by Mendis at second slip.
Angelo Mathews, who opened the bowling with Lakmal at start of play, sent down five overs for nine runs and dismissed nightwatchman Duanne Olivier.
Brief scores
South Africa - 426 (Duminy 155, Amla 134, Pradeep 4-78, Kumara 4-107)
Sri Lanka - 80 for 4 (Mendis 41)
Status - Sri Lanka trail by 346 runs
