Bains cracked 14 fours and seven sixes to notch up a whirlwind 134 in just 89 deliveries and along with his opener partner Akhil Herwadkar (88) forged a match-winning 218 partnership to take India home in just 28 overs.
This was India's fourth victory on the trot and the hosts made it to the final without losing a match and with two more games left to play.
After Zimbabwe skipper Malcolm Lake won the toss and elected to bat, seamer Atit Sheth (3 for 36) led a disciplined Indian bowling attack to restrict the visitors to 245 for nine in their stipulated 50 overs.
Abhimanyu Lamba took two for 55, while Kuldeep Yadav, Deepak Hooda and Ricky Bhui claimed a wicket each.
India got off to a flying start as Bains and Herwadkar scored runs at will, hitting a flurry of boundaries and sixes at the Port Trust Diamond Jubilee Stadium.
Bains was the more dominating between the two as he showed little respect for the visiting bowlers, plundering them all over the park as India always kept more than eight runs per over.
He was finally dismissed in the 25th over with Malcolm Lake taking the prized wicket. Herwadkar then ensured India reach home without any hiccup.
Earlier, debutant C Chitumba was the highest scorer for Zimbabwe as he hit 13 fours in his 80-ball innings of 83. Wicket keeper Joylord Gumbie was the other notable contributor with 60 runs. He had 10 fours in his 104-ball stay.
Electing to bat, Zimbabwe lost an early wicket when Atit Sheth dismissed opener Dylan Nel (4) in the second over. Lake and Gumbie then tried to steady the innings but the former was sent packing by Abhimanyu Lamba with Shreyas Iyer taking the catch.
Gumbie and Chitumba then added 88 runs in 21 overs for the third wicket to take the visitors past the 100-run mark. But soon Gumbie was shown the door by Sheth, who trapped him in front of wicket.
Next batsman Ryan Burl (11) also could not stay longer as he was removed by Bhui with Sheth taking the catch as Zimbabwe slipped to 155 for four in 34.4 overs.
Within four overs, Chitumba too was dismissed by Kuldeep, while Kieren Geyle was run out by Zope in the 43rd over. In the next seven over, Zimbabwe lost Carl Mumba (9), Luke Jongwe (34) and Brandon Diplock (8) as the visitors were restricted within 250.
Image: Ankush Bains
Photograph: Andhra Cricket Association