The Proteas, chasing a modest victory target of 104 after opting to bowl first and restricting the Dutch to 103, looked to be in peril after slumping to 12-4 after 4.3 overs at the Nassau County International Cricket Stadium.
But David Miller's unbeaten 59 steadied the ship and dragged South Africa over the line as they finished on 106-6 with seven balls to spare.
South Africa named an unchanged starting line-up following their opening victory over Sri Lanka.
The Netherlands also put trust in the same team that defeated Nepal earlier this week.
Playing XIs
South Africa: Quinton de Kock (wk), Reeza Hendricks, Aiden Markram (capt), Heinrich Klaasen, David Miller, Tristan Stubbs, Marco Jansen, Keshav Maharaj, Kagiso Rabada, Anrich Nortje, Ottneil Baartman
Netherlands: Max O'Dowd, Michael Levitt, Vikramjit Singh, Scott Edwards (capt, wk), Teja Nidamanuru, Bas de Leede, Sybrand Engelbrecht, Logan van Beek, Tim Pringle, Paul van Meekeren, Vivian Kingma