Yadav has been called up as a replacement for off-spinner Washington Sundar, who has tested positive for COVID-19.
Sundar was supposed to travel to Cape Town on Wednesday to join up with the rest of the ODI squad, but he will now remain in India.
Fast bowler Saini has also been added as back-up for Mohammed Siraj, who is still recovering from a hamstring injury he sustained in the second Test against South Africa last week.
The series starts next Wednesday at Boland Park in Paarl.
India ODI squad to face South Africa:
KL Rahul (captain), Jasprit Bumrah, Shikhar Dhawan, Ruturaj Gaikwad, Virat Kohli, Suryakumar Yadav, Shreyas Iyer, Venkatesh Iyer, Rishabh Pant, Ishan Kishan, Yuzvendra Chahal, R Ashwin, Bhuvneshwar Kumar, Deepak Chahar, Prasidh Krishna, Shardul Thakur, Md. Siraj, Jayant Yadav, Navdeep Saini.
In the third T20I, a one-sided tussle at the Saurashtra Cricket Association Stadium, Yadav blazed his way to 112 not out from 51 balls as India piled up 228-5, setting the tourists a daunting target. He got to three figures from just 45 deliveries.
India then limited Sri Lanka to 137 all out, sealing a 2-1 series success after the teams split the first two matches, both far tighter affairs than this spectacle.
Yadav's third T20I century contained nine sixes and seven fours, as he went after Sri Lanka's attack and flayed them unrelentingly. Coming in at 52-2 after 5.5 overs, Yadav followed his 117 against England last July and his 111 against New Zealand in November with another devastatingly brutal innings.
Shubman Gill (46), Rahul Tripathi (35) and Axar Patel (21no) performed well, but it was the Yadav show and they were merely a supporting cast.
Sri Lanka needed a fast start, and they got that, but openers Kusal Mendis and Pathum Nissanka both fell with the team score at 44, and Avishka Fernando followed soon after.
Wickets kept tumbling and it became clear Sri Lanka would not find a Yadav-like effort from within their ranks, with Arshdeep Singh finishing the rout by bowling Dilshan Madushanka to complete match-best figures of 3-20.
Sri Lanka find no answer to India assault
This was India's fourth-biggest win, by runs, in T20Is. Their heaviest win remains the 143-run victory over Ireland in Dublin in 2018, followed by a 101-run win over Afghanistan in Dubai in 2022 and a 93-run success against South Africa in 2017.
Yadav closes in on Rohit
India captain Rohit Sharma, who has missed this series with a finger injury, is the only man to have hit more T20I centuries than Yadav, who showed why he is number one on the ICC T20I batting rankings.
Rohit has four tons in the short format, with Yadav now one of four men with three by his name, along with Australia's Glenn Maxwell, New Zealand's Colin Munro, and Sabawoon Davizi, who has achieved the feat with the Czech Republic.
The hosts posted 159-5 off their 20 overs after winning the toss and choosing to bat.
Brandon King led the way with a run-a-ball 42 while Captain Rovman Powell made a rapid 19-ball 40* including one four and three sixes.
Kuldeep Yadav took 3-28 from his four overs for India.
India’s chase started shakily with the wickets of debutant Yashasvi Jaiswal and Shubman Gill within the first five overs.
Suryakumar Yadav and Tilak Varma then combined to put on a match-winning 87-run third wicket partnership.
Yadav led the way with a shot-filled 44-ball 83 including 10 fours and four sixes while Varma ended 49* off 37 balls.
Captain Hardik Pandya also chipped in with 20* off 15 balls as India finished 164-3 off 17.5 overs.
Alzarri Joseph took 2-25 from his four overs for the Windies.
The West Indies now have a 2-1 lead in the series heading into the final two games.
The series will now move to Florida for the fourth and fifth T20Is on Saturday and Sunday, respectively.
Having already lost the series heading into the final match on Sunday, West Indies had their tails up when they had India on just 93-4 towards the end of the 14th over in Kolkata.
Ruturaj Gaikwad – one of four changes for the hosts – was dismissed early on, with Shreyas Iyer falling to Hayden Walsh (1-30) on 25, and Roston Chase (1-23) sending Ishan Kishan packing for 34.
Captain Rohit managed just seven, yet Yadav and Venkatesh Iyer combined to hit 86 in the final five overs to reach 184-5.
Yadav's brilliant knock was ended by Romario Shepherd (1-50) on 65 from just 31 balls, as Venkatesh Iyer finished unbeaten on 35.
Deepak Chahar (2-15) took two early wickets to immediately put the Windies on the back foot, only to pull up with an injury and be forced off.
Rovman Powell's 25 off 14 got the run rate up, but he fell in the seventh over, with captain Kieron Pollard (five) swiftly following.
Jason Holder (two) and Chase (12) also went in quick succession, though Nicholas Pooran (61) stayed in to give the Windies hope.
However, Shardul Thakur (2-33) undid the Windies opener in the 18th over, all but ending any lingering hopes.
Stunning late show from India pair
There was some sensational batting on show from Yadav and Venkatesh Iyer, who hit seven and two sixes respectively. They added 91 off 37 deliveries to put the game, truly, beyond the West Indies' reach.
With the ball, Harshal Patel took 3-22 to pick up the slack after Chahar's injury.
India on a roll
India have now won 13 T20Is against the West Indies, only against Sri Lanka (14) have they won more.
Indeed, they also extended their winning streak in the format to nine games, their longest such run in the format. They will go up against Sri Lanka in their next series.
Test cricket's most prolific pace bowler was staggered to be carved away to the boundary in such an unorthodox manner, as India got the better of England on day two in Ahmedabad.
Anderson had only just taken the new ball and had seen it already thrashed to the boundary by Pant from successive balls.
On his way to 101, Pant decided the moment was ripe to paddle Anderson over the England slips for one of the most remarkable shots likely to be played in a Test.
The fourth and final match of the series is leaning heavily India's way after they reached the close on 294-7, with a first-innings lead of 89 runs.
Pant said of his special shot: "You have to premeditate that, but when everything is going your way you can try your luck sometimes."
Quoted in the Times of India, he said: "I get the license most of the time, but I have to assess the situation and take the game head on. I like to make the team win and if the crowd is entertained by that, I'm happy."
Pant came to the crease with India in trouble on 80-4, and they were also stumbling at 146-6, but his alliance with Washington Sundar (60 not out) turned the momentum of the game.
Anderson eventually took revenge, having Pant caught by Joe Root to end a 118-ball innings, but it was the batsman's day after he began with a cautious approach.
"If the bowlers are bowling well, respect it and take the singles, and that was on my mind," Pant said. "I like to play the situation and I just see the ball and react - that's the USP of my game.
"The team plan was to get to 206, past the England total, and then get as many runs as possible after that as a batting unit."
The relatively inexperienced India team ended a 32-year unbeaten run for the Aussies on the back of a stellar innings from Rishabh Pant. The team’s performance broke Australian hearts, and records as well, with the mammoth target of 328 runs representing the highest ever successful runs chase at the venue. It was achieved with 3 wickets remaining.
Heading into the series as huge underdogs, the team owed a large part of the victory to resilience, Shubman Gill's crucial 91 and the dogged determination of Cheteshwar Pujara who faced 211 deliveries and 10 body blows to defend the Border-Gavaskar trophy on a dramatic final day.
For, Mohammed, who will lead a hastily assembled and likewise inexperienced squad against Bangladesh, starting on Wednesday, there is plenty about the India performance to draw encouragement from.
“It’s obviously something we will look to. It depends on the day and how you play,” Mohammed told members of the media via a press conference call on Tuesday.
“A lot of the guys will be making their debut, but once you have that belief and belief within the team that you can do well and that you can win games then these things are achievable and it showed in the India versus Australia series,” he added.
“We have the same mindset. We are just looking to play some good cricket starting tomorrow and hopefully, the results will be on our side as well.”
