Sri Lanka's chase was interrupted by rain at the Wanderers in Johannesburg but the tourists were well behind the rate by then as South Africa went on to win the match by 45 runs via DLS.
The victory at SuperSport Park was set up by half-centuries from opener Reeza Hendricks (65 off 46 balls) and Rassie van der Dussen (64 off 44).
South Africa clawed its way to 134/8 to force the Super Over after Sri Lanka had earlier posted 134/7 in Cape Town.
CSA feels that the players must finish the Sri Lanka series before they leave for India. But the players are keen to be present from the start of the 12th edition of the cash-rich league.
Hathurusingha will be returning to Sri Lanka after the final ODI game in Cape Town on March 16.
Isuru Udana made 78 from 57 balls batting at No.9 but Anrich Nortje's 3/57 and Quinton de Kock's 51 ensured South Africa beat Sri Lanka by six wickets.
South Africa's victory gave it an unassailable 3-0 lead in the five-match series and helped restore some pride after Sri Lanka pulled off a major surprise earlier in the Test series.
The result wasn't on the cards after South Africa lost their last six wickets for 21 runs to fall to a mediocre total of 251 all out batting first.
Faf Du Plessis finished on 112 not out and South Africa cruised to 232-2 to win with just over 11 overs to spare.
Lungi Ngidi had proved his fitness after recovering from a knee injury sustained last year.
South Africa won seven straight series at home before Sri Lanka, struggling for form, pulled off the first shock of the tour by chasing down 304 to win the first test and ensure they would at least draw the contest.
Vishwa Fernando and Kasun Rajitha shared six of the wickets as the tourists continued to defy pre-series predictions that they'd be easily overpowered in South Africa.
Chasing an unlikely 304, Sri Lanka was 226-9 and looked out of it at Kingsmead with the 10th wicket an apparent formality.
Perera almost single-handedly won the game but No. 11 batsman Vishwa Fernando played a crucial role as he hung around for 27 balls for his 6 not out to allow Perera, with nothing to lose.
Sri Lanka need another 221 runs with seven wickets left at a ground where there have been only four previous fourth-innings totals in excess of 300 in nearly 100 years of test cricket.
On Thursday, Steyn bowled a fiery unbroken 10-over spell with speeds constantly in the high 140s.
Steyn was instrumental in bowling Sri Lanka out for 191 to see South Africa hold a 44-run first-innings lead.
Sri Lankan bowlers set the tone for the visitors by wrapping up the hosts cheaply on day one of the first Test in Durban.
Chandimal's omission follows scores of 5, 0, 15, and 4 in the two recent Test losses against Australia.
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