Captain Chamari Athapaththu top-scored with 68 and shared in an 86-run stand for the second wicket with Vishmi Gunaratne (35) as Sri Lanka made 129 for four after being sent into bat at Newlands.
South Africa began well in their reply but lost wickets at regular intervals and, despite needing 20 off the final two overs with four wickets in hand, fell just short of their target on 126 for nine.
Veteran slow left-armer Inoka Ranaweera starred with the ball for Sri Lanka, claiming three for 18 off her four overs including the key wickets of Laura Wolvaardt, Marizanne Kapp and captain Sune Luus.
After losing the toss, Sri Lanka made a steady start with an opening partnership of 28 before Nadine de Klerk provided the breakthrough for South Africa with the wicket of Harshitha Samarawickrama, who spooned one up to Tazmin Brits at short mid-wicket.
However, that was as good as it got for the tournament hosts early on as Athapaththu and Gunaratne joined forces to frustrate their opponents before both fell in successive balls in the 18th over.
Gunaratne was run out and Athapaththu, who struck 12 fours in her 50-ball knock, was then caught by De Klerk off the bowling of Kapp.
South Africa ensured there were no late Sri Lanka fireworks after that with some superb death bowling by Kapp and Shabnim Ismail, who picked up the wicket of Nilakshi de Silva.
Still overwhelming favourites for victory, South Africa’s openers were progressing well with a stand of 29 in 4.4 overs when Oshadi Ranasinghe (two for 20) snared Brits for 12 with a leading edge.
Wolvaardt, Kapp, Luus, Chloe Tryon and Sinalo Jafta all reached double figures for South Africa but nobody could really go on as Sri Lanka kept them in check.
From a position of strength at 44 for one, South Africa slumped to 72 for five and suddenly Sri Lanka looked capable of a surprise victory.
The Proteas needed 33 from the last 18 balls but the wickets of Jafta (15) and skipper Luus (28) proved to be the final nails in the coffin as Sri Lanka picked up the competition’s first victory.
