India seamer Jasprit Bumrah took 6-61 to bowl South Africa out for 176 in their second innings on the stroke of lunch on the second day, before the visitors came out swinging and completed the win in 12 overs as they reached 80 for three.
Bumrah bowled a superb probing line but also profited from poor shot selection by the home batters, who seemed in a hurry to score runs on a difficult wicket.
Rohit Sharma finished not out on 16 and Shreyas Iyer on four, with Yashasvi Jaiswal (28), Shubman Gill (10) and Virat Kohli (12) being the other wickets to fall.
There will be plenty of scrutiny of the Newlands pitch with the match completed in 642 balls, the shortest ever test in which there has been a winner, beating Australia’s 656-ball victory over South Africa in 1932.
"Obviously it's a great feat, but having said that we had to learn from whatever mistakes we made (in the first test)," India captain Rohit Sharma said.
"The bowlers still have to put the ball in the right areas and the boys got rewarded for it. When you come to this part of the world, it's always difficult but we take pride in our performance outside of India."
South Africa opener Aiden Markram blasted a quick-fire 106 from 103 balls as he defied the conditions but lost partners at regular intervals, which forced him to launch a blistering assault with the bat.
After South Africa resumed their innings on 62-3, David Bedingham was Bumrah’s first victim in the opening over of the morning as he chased a delivery outside off-stump and was caught by wicketkeeper KL Rahul for 11.
Kyle Verreynne tried an ill-advised pull and was caught at mid-on by Mohammed Siraj for nine, before Marco Jansen was caught and bowled by Bumrah for 11.
Keshav Maharaj became the seamer’s fourth victim of his spell when he guided a delivery to Shreyas Iyer at slip when he had three.
Markram took the attack to India and it worked as he raced to his century in 99 balls but played one big shot to many as he skied a Mohammed Siraj delivery to Rohit Sharma at mid-off to end an innings of 17 fours and two sixes.
South Africa eked out a further 14 runs before Bumrah claimed his sixth wicket to end the home side's resistance and India chased down the total with the minimun of fuss.
"A tough one for us, we were positive coming into the game, but the first innings with the bat ... India bowled well and used the conditions to a tee," retiring South Africa captain Dean Elgar said.
"It (the wicket) was a bit of a ripper, to the naked eye it looked a nice one, but it played different to what everyone thought it would play.
"I still don't regret my decision to bat first but they outskilled us in the first session."
