Bangalore skipper Kohli showed patience at the start as he brought up his fifty in 40 deliveries but it took him only another 17 balls to reach his century. His previous four IPL hundreds all came in 2016.
The 30-year-old smashed nine fours and four sixes before he fell to the final ball of the Bangalore innings.
England all-rounder Moeen Ali also played a blistering knock of 66 off 28 balls, hitting six sixes and five fours to seize momentum for his team.
Kolkata came close thanks to a 118-run partnership between Nitish Rana (85 not out)and Windies power-hitter Andre Russell (65) but finished on 203-5, 10 runs short of Bangalore's total.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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