Seamer Ngidi, 21, recorded figures of 6-39, his best in first class cricket, as South Africa bowled out India for 151 just before lunch.
India are the top-ranked side in test cricket according to the International Cricket Council (ICC) rankings with South Africa second, though the Proteas will not be able to overhaul the sub-continent side even with a 3-0 series win.
The third test starts at the Wanderers in Johannesburg on Jan. 24.
"It took a lot of hard work and was one of the harder test matches in terms of what you had to put in," South Africa captain Faf du Plessis said at the post-match presentation.
"Bowling was tough, batting was tough, but over the five days I thought we were on top most of the time."
India resumed the final day on 35 for three chasing a victory target of 287, having been dealt a huge blow the evening before when Ngidi bagged the wicket of captain Virat Kohli (5).
Their slender hopes were dealt a further set-back when Cheteshwar Pujara (19) became the first Indian player ever to be run out twice in a test.
Ngidi had a hand in that too as he chased the ball down to the boundary and stopped a four, with his cut-back to AB de Villiers allowing for a bullet throw to wicketkeeper Quinton de Kock that saw Pujara short.
Pujara had also been run out first ball in the first innings and has now been involved in six of India's last eight run-outs in tests.
It would start a procession of wickets as Parthiv Patel (19) picked out Morne Morkel on the fine leg boundary off Kagiso Rabada (3-47), with the big fast bowler pulling off a magnificent catch on the run.
Hardik Pandya (6) was caught by De Kock off Ngidi, before the seamer also induced an edge from Ravichandran Ashwin (3) to the wicketkeeper to leave India reeling at 87 for seven.
Rohit Sharma (47) took the attack to the bowlers before he was magnificently caught at fine leg by De Villiers off Rabada attempting a hook.
The innings wrapped up quickly after that, as Mohammed Shami (28) was caught by Morkel off Ngidi and Jasprit Bumrah spooned a catch to Vernon Philander at mid-off to hand the youngster his sixth wicket and debut match figures of 7-90.
"We thought the wicket was really flat to play on, it was quite surprising," Kohli said. "We tried our best but South Africa were better than us in every department, especially fielding."
(Reporting By Nick Said; Editing by Christian Radnedge)
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