Leading 1-0 at half-time, courtesy of Sulette Damons's 11th minute strike, Ireland grabbed a superb equaliser through Anna Flanagan 11 minutes into the second period.
Dirkie Chamberlain regained South Africa's lead five minutes later, but Audrey O'Flynn pulled level for a second time shortly before the hour mark to round off an exciting opening encounter.
"We weren't good enough in the end zone [in both attack and defence] and gave away too many corners in the second half," South Africa's coach, Giles Bonnet, said after the game.
"We created enough chances, but you've got to put them away if you want to win.
"I was happy with how we played to get the ball there, we had very many scoring chances, but you've got to score then, and that's the difference.
"It would have made an interesting scoreline but the final finishing was poor today."
Bonnet added that despite dominating for the majority of the game, Ireland took their chances and were clinical in front of goal, as opposed to South Africa, who squandered several opportunities.
"They did not have many goalshots, but we must finish, and that's it," Bonnet said.
The South Africans next meet world number 10-ranked United States on Monday, before a tough encounter with Spain lies in wait later next week.
Earlier on Sunday, the US eased past Spain 3-1.
Scorers: South Africa (1) 2: Sulette Damons (11th minute), Dirkie Chamberlain (49th minute)
Ireland (0) 2: Anna Flanagan (44th minute), Audrey O'Flynn (58th minute)