Zimbabwe were dismissed for 216 in the second innings, leaving the Mohammad Kaif-led A team with a target of 65, which Team India discard Irfan Pathan and Rohit Sharma rattled off for the loss of just opener Robin Uthappa's wicket.
Needing 136 more runs to avoid an innings defeat, Zimbabwe resumed the last day's play at 15 for one in the second innings with hopes of batting out the entire day to force a draw.
But Pathan struck early, removing opener Hamilton Masakadza early. After that there was a lull as Indian pacers toiled away without success for a long time through a 108-run partnership between Vusi Sibanda (69) and Tatenda Taibu (40) before the young Piyush Chawla got into the act.
He grabbed four wickets that included Sibanda, Taibu and Elton Chigumbura (30) to propel India towards victory. Mumbai's Romesh Pawar chipped in with two wickets and Rohit Sharma took one wicket while VRV Singh added another wicket to his overnight victim.
Pathan, then opened in the second innings, hitting a breezy 30-ball 39 to take India home.
Earlier replying to India's 489 all out, Zimbabwe were dismissed for 338, just two runs short of avoiding a follow on, with overnight batsman Taibu doing bulk of the scoring to come up with a defiant 123 off 245 balls, studded with 11 fours.
Chawla was the star performer for India 'A' in the first innings too, snapping up 4 for 40 off 22 overs while Pathan and Yo Mahesh picked up two wickets apiece.
''We started very well in the morning with Sibanda and Taibu getting quick runs but everything crumbled once Taibu fell,'' Zimbabwe Cricket spokesman Blessing Maulgue told VOA.
''The experienced guys need to pull up the socks. Only Taibu performed in the first innings. The guys like Masakadza, Sibanda and Chigumbura need to perform consistently and our batsman have to give something for our bowlers to defend,''Maulgue said.
The two sides will now square up in the second and final four-day game at Queens Sports Club in Bulawayo starting on Tuesday.
Brief Scores: India A 489 (Uthappa 88, Patel 67, Sharma 66) and 69 for 1 (Pathan 39 n o) beat Zimbabwe Select 338 (Taibu 123, Utseya 53, Chawla 4 for 40) and 216 (Sibanda 69, Taibu 40; Chawla 4 for 30) by 9 wickets.