Wicketkeeper Kishan made 81 off 44 balls and unbeaten Varma 60 from 29 deliveries at Harare Sports Club as the tourists took an unassailable 2-0 lead. The final match is scheduled for Sunday.
A second victory in three days marked a turnaround for India, who arrived in southern Africa after series losses in Ireland and England.
Sooryavanshi, the 15-year-old batting prodigy who scored his maiden T20I half-century on Thursday in Harare, scored 20 runs.
Put in to bat, India posted 219-5 with whirlwind stands of Kishan and Varma tormenting the Zimbabwe bowlers. Zimbabwe were all out for 129 in reply.
Batting at No. 3, Kishan put on 66 runs for the third wicket with captain Shreyas Iyer (25) and 95 for the fourth with Varma.
Kishan struck two sixes and nine fours before slicing a Newman Nyamhuri delivery outside off stump. Brian Bennett darted forward from deep to pull off a superb catch.
Varma, like Kishan, part of the 2026 T20I World Cup-winning team, struck three sixes and five fours in his undefeated knock.
Sooryavanshi hit a six and three fours off nine balls before a sliced a pull off a Richard Ngarava delivery was caught by Blessing Muzarabani retreating from mid-on.
Zimbabwe lie 10 places below India in the world T20I rankings and were always struggling, with only opener Bennett (32) and wicketkeeper Tadiwanashe Marumani (24) enjoying some batting success.
Yash Thakur claimed his first T20I wicket by dismissing Bennett. His delivery outside off was lobbed behind the stumps, and Kishan made a simple catch.
Left-arm spinner Abhishek Sharma (3-17), another 2026 T20I World Cup winner, was the most successful Indian bowler.