Chasing 287, India were bundled out for 151 in 50.2 overs.
Resuming the day at 35 for three, India failed to recover in their second innings and surrendered to a potent South Africa pace attack.
Lungi Ngidi was the pick of the bowlers for South Africa, picking up a six-wicket haul in the innings and a match haul of seven on debut.
India had lost the first Test by 72 runs at Cape Town.
The third and final Test will be played in Johannesburg from January 24.
South Africa 1st innings: 335
India 1st innings: 307
South Africa 2nd innings: 258
India 2nd innings: 151 in 50.2 overs (Sharma 47; Ngidi 6/39).
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