Springbok captain Siya Kolisi said New Zealand had taken his side to a "dark place" in the Rugby World Cup final, but praised his South Africa side for finding a way to win a record fourth title.
The Boks had led 12-6 at halftime in Paris, Handre Pollard kicking four penalties to two from Richie Mo'unga.
The sole score of the second half was a Beauden Barrett try for a New Zealand team reduced to 14 after Sam Cane was red-carded for a high tackle after 34 minutes.