After Sunday's opener in Dharamsala was washed out, the home team did well with the ball to restrict the Proteas to 149-5, Quinton de Kock top-scoring with 52.
Not for the first time in his career, Kohli timed the chase superbly, keeping the run-rate under control before accelerating late on to see his team cruise over the line in Mohali with six balls to spare.
His 22nd score of 50 or more for India in the T20 format saw him move past team-mate Rohit Sharma, who made 12 before he was trapped lbw by Andile Phehlukwayo, atop the list of leading run-scorers at international level.
Shikhar Dhawan contributed 40 before falling to a sensational catch in the deep by David Miller, the fielder at long on motoring to his right before clinging onto the ball with one hand as he put in a full-length dive.
Still, the stunning piece of fielding, plus the dismissal Rishabh Pant (4), failed to inspire South Africa, with the masterful Kohli, whose innings spanned 52 deliveries, seeing India to their target.
Another record broken!
Virat Kohli has now scored more runs in men's T20Is than any other cricketer pic.twitter.com/1fBBGJjyOQ
— ICC (@ICC) September 18, 2019
Visiting skipper De Kock had earlier hit eight boundaries in a 37-ball knock that was ended by a fine running catch by his opposite number, leaving the score at 88-2.
Temba Bavuma marked his international T20 bow with 49, but South Africa's middle order struggled to up the tempo in the second half of their innings.
Deepak Chahar removed the well-set Bavuma as he finished with impressive figures of 2-22, while Miller (18) was bowled by Hardik Pandya with the first ball of the 19th over.
Dwaine Pretorius and Phehlukwayo both hit huge sixes in the closing stages, but South Africa’s total always looked to be under par. They will now aim to draw the series when the teams meet again on Sunday, this time in Bangalore.
Photo Getty Images. Caption: India Captain Virat Kohli