India won the toss and chose to bat in their bid for a third straight win but the South African quicks made life difficult on a fast and bouncy Perth pitch.
Yadav's 40-ball 68, laced with six fours and three sixes, helped India recover from 49-5.
Ngidi returned figures of 4-29 off his four overs, ably supported by fellow fast bowler Wayne Parnell who finished with 3-15 after starting the innings with a T20 rarity - a maiden over.
Skipper Rohit Sharma hit a six and a four before being caught and bowled by Ngidi, who returned to the side as South Africa's only change.
He got KL Rahul next for nine but the big wicket came when Ngidi sent back Virat Kohli for 12, caught in the deep, to silence an Indian-dominated crowd.
Unable to handle the extra bounce on the Perth track, the Indians lost half their side for 49 inside nine overs.
Kagiso Rabada took a stunning catch at long leg to see the back of danger man Hardik Pandya for Ngidi's fourth wicket.
Yadav hit back with a couple of sixes as he rebuilt the innings with Dinesh Karthik.
The in-form Yadav, who hit an unbeaten 51 against the Netherlands in their previous win, even smashed Ngidi for a huge six over fine leg to bring alive the fans. He then reached his fifty off 30 balls with another four.
Karthik tried to join the attack but fell to Parnell, who broke the stand which had been worth 52 and the same bowler finally dismissed Yadav for 68 in the 19th over.
The Proteas need 134 runs to win and stay unbeaten in the tournament after a washout in their opening match against Zimbabwe and a big win against Bangladesh.
