After Zimbabwe were sent in to bat on Thursday, the home side managed 125 for seven in their 20 overs, a total that was never likely to trouble the tourists, who chased it down with 40 balls remaining.
The 15-year-old Sooryavanshi was at his destructive best as he hit four fours and four sixes on the large Harare Sports Club ground before being caught at deep third man off a top edge from the bowling of Richard Ngarava (1-30).
Sooryavanshi improved his previous best score of 15 after he debuted in England earlier this month but found the going tough.
"I think the boys were tremendous," India captain Shreyas Iyer said.
"Couldn't have been happier with my first win (as captain). There was bounce from good length and it was also variable.
"We are going to play two more matches here, so today's performance gives everyone some confidence. I think Vaibhav has played here, he got 175 in the under-19 World Cup final, so he knows the conditions."
Iyer chipped in with an unbeaten 28 from 24 balls and Ishan Kishan managed 35 from 24 deliveries as India coasted home.
Wessly Madhevere (39 runs from 34 balls) was the only Zimbabwe batter to post a score of substance.
Batter Ben Curran (10) and medium pacer Newman Nyamhuri (0-30) made their T20 debuts for the home side, with seamer Ashok Sharma (0-29) also appearing for the first time in international cricket for India.
The second match is scheduled for Saturday and the three-game series will conclude a day later. Both fixtures are in Harare.
