Kohli hit three sixes and seven fours after proceedings were delayed by five hours as India made 164-6.
He shared stands of 49 with Rahul Dravid (15) and 69 with Rohit Sharma (30).
In reply, Joe Denly made 100 for Kent, with three sixes and eight fours, off 67 balls.
But once he was bowled by RP Singh in the 19th over, Kent were unable to get over the line and only three runs came off the final over.
India, who lost the Test series to England by 4-0, next face Leicestershire in a Twenty20 game on Monday before facing the English at Old Trafford in another T20 on Wednesday.
Copyright AFP (Agence France-Presse), 2011