Jaiswal, who played second fiddle in an opening stand of 155 with Rohit Sharma (75), smashed an unbeaten 116 as India chased down a 271-run target with more than 10 overs to spare on Saturday, with the on-song Virat Kohli again also making key runs.
"The most pleasing thing about the series, is how we held our nerve," India captain KL Rahul said at the presentation ceremony.
"South Africa came out with an intent to put us under pressure, one result didn't go our way but we weren't too upset."
Earlier, Quinton de Kock struck a brisk 106 but South Africa were dismissed for a below-par 270 in the 48th over.
In a notable prelude, India ended a luckless sequence of 20 consecutive lost tosses in ODIs.
Skipper Rahul punched the air to celebrate that and elected to field to spare his bowlers the predicament of having to operate with a wet ball once the evening dew set in.
South Africa's innings began shakily with the early departure of Ryan Rickelton but de Kock and Temba Bavuma, who made 48, forged a century stand to steady their innings.
Ravindra Jadeja removed Bavuma before Prasidh Krishna (4-66), who bled 27 in his first two overs, returned to dismiss Matthew Breetzke, Aiden Markram and de Kock in a decisive match-turning spell.
Left-arm wrist-spinner Kuldeep Yadav (4-41) then cleaned up the tail, consigning South Africa to their first sub-300 total of the series.
India, who lost the preceding tTst series 2-0, began strongly in their chase.
The 38-year-old former India captain Rohit compiled his fourth fifty-plus score in five innings, anchoring a big opening stand with Jaiswal, who was happy to bide time at the other end.
Rohit departed after fluffing his slog-sweep against spinner Keshav Maharaj but Jaiswal went on to become the sixth Indian to hit a hundred in all three international formats of the game.
Kohli, now active exclusively in the ODI format like Rohit, walked out to thunderous applause and made a typically fluent 65no, which followed his hundreds in Ranchi and Raipur.
"Playing the way I have in the series is the most satisfying thing for me," player-of-the-series Kohli said after ending the series with a stunning average of 151.
"I feel really free in my mind. I haven't played like this in two, three years."
