Mohammed Shami gave India a fine start to Day 4, picking two early wickets.
Jasprit Bumrah showcased his red-ball prowess with the white ball to rattle South Africa further.
Bhuvneshwar Kumar too picked wickets as South Africa failed to stop the rut.
AB de Villiers forged a lone battle but that didn't last as long as he would've liked.
India picked eight wickets for 65 runs in the morning session to bowl out SA for 130. India were thus, set a target of 208.
Shikhar Dhawan was undone by extra bounce on a back-of-a-length ball from Morne Morkel and fell early.
After losing three early wickets, Kohli and Rohit looked to steady India's innings.
Philander dismissed the Indian captain and Rohit Sharma to derail India's chase.
Kagiso Rabada chipped in with wickets too, as India went into Tea break with only three wickets in hand.
Despite some defiance from Ashwin and Bhuvneshwar Kumar, Philander broke through, picked the last three wickets and earned South Africa a 72-run victory.