With just six points from seven games, Sri Lanka still have a mathematical chance to be in the semifinals. First, they need to win their last two games against already-eliminated West Indies (on July 1) and India (July 6) and then depend on favourable results from other remaining league stage games.
On the other hand, the win, however, came as a welcome relief for South Africa, who have endured a nightmarish World Cup campaign.
The Proteas are already out of the tournament after registering just two wins out of their eight games.
Chasing the modest target, South Africa lost Quinton de Kock (15) at the score of 31 in the fifth over but thereafter Hashim Amla and skipper Faf du Plessis held the fort and stitched an unbeaten 175-run stand to guide the Proteas home comfortably.
While Du Plessis remained unbeaten on 96 off 103 balls, hitting 10 boundaries and one six, Amla finished on 80 not out off 105 balls with the help of five fours.
Lasith Malinga (1/47) was the only successful bowler for Sri Lanka.
Earlier, the Proteas picked up wickets at regular intervals after the first 10 overs, never allowing the Sri Lankan middle-order settle down. Drafted into the playing eleven in place of Lungi Ngidi, pacer Dwaine Pretorius (3/25) justified his selection with a three-wicket haul.
Chris Morris (3/46) and Kagiso Rabada (2/36) shared five wickets between them.
Right-arm pacer Pretorius sent both the batsmen packing in consecutive overs as Sri Lanka slumped to 72 for three in 11.3 overs.