The home team, after winning toss and opting to bowl first, caused havoc for the Proteas' top order in the early stages as they lost their first five wickets with just nine runs on the board in the third over.
With four of the top six batters out for ducks, the visitors were always going to struggle to put a substantial total together and eventually made their way to 106-8 in their 20 overs.
India lost two early wickets in the run-chase as Kagiso Rabada dismissed Rohit Sharma and Anrich Nortje took the scalp of Virat Kohli as the conditions continued to favour the quick bowlers.
KL Rahul (51 not out) and Suryakumar Yadav (50 not out) made sure there were no further dramas though as they knocked off the required runs with more than three overs to spare.
India's opening bowlers Arshdeep Singh and Deepak Chahar started all the carnage as the latter clean-bowled captain Temba Bavuma for nought in the first over.
Quinton de Kock (1) was next to walk back to the dressing room as the left-hander inside-edged onto his stumps from Arshdeep and then had Rilee Rossouw caught behind in the same over for a single.
The procession of wickets continued when David Miller had his stumps castled first ball while Tristan Stubbs was caught at third-man.
The tourists did well to launch some sort of recovery from the horror start with number eight Keshav Maharaj hitting fighting 41 off 35 balls.
Aiden Markram (25 off 24) and Wayne Parnell (24 off 37) also fought hard with the willow but the damage done earlier was just too much to haul in.
India's left-arm seamer Arshdeep finished with man-of-the-match figures of 3-32 in his four overs while right-arm paceman Chahar took 2-24.
The Proteas now must win the second game on Sunday in Guwahati to stay in the three-match series.