Having started day four 150 runs ahead on 11-0 in Colombo, Sri Lanka increased their advantage to 368 runs after declaring on 229-8.
The experience of veteran Kumar Sangakkara (72) and captain Angelo Mathews (63 not out) proved pivotal to Sri Lanka as they bid to try and rescue the two-match series.
Morne Morkel starred with the ball for South Africa, recording figures of 4-45, and although a 2-0 success now seems highly unlikely - the visitors ended Sunday 38-1, requiring another 331 runs for victory - they need to bat out the final say to secure the series win.
South Africa's reply started poorly as opener Alviro Petersen went for a duck, but Dean Elgar (13 not out) and Quinton de Kock (21 not out) stabilised the situation.
That pair guided South Africa to 38-1 before a combination of bad light and inclement weather forced the umpires to bring play to a close.
Earlier in the day, Sri Lana's openers put in a below-average display as they looked to put further pressure on South Africa.
Upul Tharanga (30), Kaushal Silva (26) fell cheaply, as did Mahela Jayawardene (0), as the home team were reduced to 83-3.
But any hopes of a South Africa triumph were effectively ended by an excellent fourth-wicket partnership of 81 between Mathews and Sangakkara.
Morkel ended that stand by dismissing Sangakkara, but Mathews remained defiant to help guide Sri Lanka past 200.
The skipper found little in the way of support from the lower order, though, with his declaration arriving after Rangana Herath (4) became Morkel's final victim.
Herath (1-7 from eight overs) - who took four wickets in the first innings' demolition of South Africa - did not need long to strike with the ball, Petersen pushing a turning delivery to Kithuruwan Vithanage at silly point.
Wicketkeeper De Kock was brought up to three following that dismissal, and recovered the situation slightly for South Africa before their chase was brought to a halt by the changing conditions.