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.