After being sent in to bat, India reached 201 for seven in their 20 overs at The Wanderers, before they dismissed the home side for a paltry 95.
Yadav anchored the innings with a sublime century in which he struck boundaries in all parts of the ground, with seven fours to go with eight sixes for his fourth century in international T20 matches.
He put on 112 for the third wicket with opener Yashasvi Jaiswal, who also impressed with 60 from 41 balls after India had lost Shubman Gill (8) and Tilak Varma (0) in consecutive balls off the bowling of excellent spinner Keshav Maharaj (2-26) with the score on 29.
Rinku Singh (14) was the only other batter to get into double figures in India’s total.
The visitors' seamers got more movement off the wicket from the start and South Africa never looked settled in their chase before the spinners finished them off.
Only David Miller offered any real resistance with 35 from 25 balls before he was the last man out, giving wrist-spinner Kuldeep Yadav career-best figures of 5-17 in 2.5 overs.
There was a major worry for the tourists when Suryakumar Yadav rolled his ankle while attempting a routine piece of fielding and had to hobble off. There was no immediate news on the extent of the damage.
The two sides begin a three-match One-Day International series on Sunday at the same venue, before further matches in Gqeberha on Tuesday and Paarl next Thursday.
