The visitors rattled up 161 for 5 after being put in to bat, and then bowled with discipline to restrict the domestic T20 champions to 146 for 7 in the stipulated 20 overs.
This is India's third successive victory in practice games, ahead of the the one-off Twenty20 and five One-Day Internationals against England [ Images ].
Vinay was the hero of India's victory, conceding only 29 runs from his four overs and picking three smart wickets.
The Indians got their runs collectively, with openers Parthiv Patel [ Images ] (40) and Ajinkya Rahane [ Images ] (19) providing a good start of 52 runs from 5.4 overs, and, later, Rohit Sharma [ Images ] (29) and Suresh Raina [ Images ] (21) finishing with a flourish.
In between, Rahul Dravid [ Images ] contributed 29, but his attempts at slogging didn't go with his elegant batting style.
Leicestershire lost an early wicket to Praveen Kumar [ Images ], but then Andrew McDonald (44) and Will Jefferson (20) appeared threatening for a while.
However, Vinay bowled an excellent spell in middle overs, and the two spinners, Amit Mishra [ Images ] and Ravichandran Ashwin, were excellent foil as Indians tightened the screws.
Some late hitting by Abdul Razzaq [ Images ] brought the equation to 43 off the last three overs.
Praveen Kumar, who bowled his first three overs for 16 runs, went for 10 from his final over as Leicester required 33 from the final two overs.
However, Razzaq was caught in the deep in the penultimate over, bowled by Ashwin. The Pakistan all-rounder made 37 off 24 balls, inclusive of five fours.
Ashwin conceded only eight runs from this over to make it 25 from the final over, still a difficult task for the hosts.
Vinay then bowled the final over and conceded only nine runs while claiming the wicket of Jacques du Toit (13) to clinch the game for the Indians.
Earlier, openers Parthiv and Rahane scored 52 from 5.4 overs to give India a flying start.
Patel cut Matthew Hoggard [ Images ] over slips in the very first over and hoisted Razzaq over mid-on. He then cracked Hoggard through cover and lofted Razzaq over his head.
Rahane, on the other hand, favoured the on-side for his early strokes, flicking Hoggard to fine leg and then driving Razzaq to the mid-wicket fence. The best shot of the stand, though, was when he drove Hoggard for a boundary through extra-cover.
Rahane, however, departed in the sixth over when he gave charge to Razzaq, and Jigar Naik, at short third man, held a fine catch.
Soon India lost its second opener, when Parthiv holed medium-pacer Andrew McDonald to deep midwicket.
The innings then got bogged down as the slower bowlers came into operation and the slow nature of the wicket defeated the attacking instincts of the Indian batsmen.
Both Virat Kohli [ Images ] (13) and Dravid (29), the number three and four batsmen at the crease, departed by holing out to fielders in the deep.
Rohit (29) then smacked two successive sixes to power the Indians past 150.
Raina (21), leading the side in this match, also hit some cracking blows in the end.
Rookie fast bowler Varun Aaron played his first match on the tour but was expensive, conceding 34 runs in his three overs.
Parthiv Patel c Jefferson b Mcdonald 40
Ajinkaya Rahane c Jigar Naik b Abdul Razzaq 19
Rahul Dravid c White b Cobb 29
Virat Kohli c sub b Naik 13
Rohit Sharma c McDonald b Cobb 29
Suresh Raina not out 21
Praveen Kumar not out 0
Extras: (B-5, LB-3, W-2) 10
Total: (for 5 wkts in 20 overs) 161
Fall of wickets: 1-52, 2-73, 3-102, 4-121, 5-155
Bowling: Matthew Hoggard 3-0-31-0, Abdul Razzaq 3-0-24-1, Andrew McDonald 3-0-15-1, Jigar Naik 4-0-20-1, Will White 4-0-41-0, Cobb 3-0-22-2.
Joshua Cobb b Praveen Kumar 4
Andrew McDonald b Vinay Kumar 44
Will Jefferson lbw b Mishra 20
James Taylor c Patel b Vinay Kumar 5
Paul Nixon b Amit Mishra 6
Abdul Razzaq c Kohli b Ashwin 37
Jacques du Toit b Vinay Kumar 13
Wayne White not out 2
Matthew Boyce not out 4
Extras: (LB-8, W-3) 11
Total: (for 7 wkts in 20 overs) 146
Fall of wickets: 1-4, 2-48, 3-66, 4-83, 5-94, 6-132, 7-142
Bowling: Praveen Kumar 4-0-26-1, Varun Aaron 3-0-34-1, R Ashwin 4-0-23-1, Amit Mishra 4-0-19-2, Vinay Kumar 4-0-29-3.