The Proteas, who were sent in to bat at the toss by home captain Shikhar Dhawan, were bundled out for just 99 at the Arun Jaitley stadium.
It was the second time in the space of three months that South Africa have been bowled out for less that 100 in 50-over internationals after the total of 83 against England in Manchester in July.
It was another dark day for the Proteas' batters on the India tour that has also seen the tourists conceding the three-match T20I series 2-1.
The rot started early on Tuesday as opener Quinton de Kock (5) fell in the third over with only seven runs on the scoreboard.
Fellow opener Janneman Malan's (15) poor form continued as paceman Mohammed Siraj (2-17) coaxed the batter into a hook shot that saw him caught on the square-leg boundary.
The procession of wickets continued when spin was introduced into the bowling attack as wrist-spinner Kuldeep Yadav wrecked havoc.
The left-arm tweaker finished with figures of 4-18 in 4.1 overs while fellow slow-bowlers Washington Sundar and Shahbaz Ahmed took two wickets apiece.
Heinrich Klaasen was the top-scorer in the innings with 34 before being undone by Ahmed with Malan and Marco Jansen (14) the only other batters to reach double figures.
With a target of only 100 to chase to win the series trophy, India were quickly out of the blocks with bat in hand.
Opening pair Dhawan and Shubman Gill put on 42 in the first six overs with the latter being the dominant batter in the partnership.
The home skipper was run-out for 8 while number three Ishan Kishan was caught behind off the bowling of spinner Bjorn Fortuin for just 10.
Gill made his way to 49 but was trapped lbw by paceman Lungi Ngidi, leaving Shreyas Iyer (22 not out) to hit the series-winning runs in the 20th over to wrap up a comprehensive victory.