Openers Shikhar Dhawan (69) and Rohit Sharma (46) laid a strong foundation with their 123-run stand and Kohli ensured that their hard work does not go waste as he made up for the failure of the middle-order with his gritty knock.
Kohli got out in the last ball of the innings as he nullified the success of West Indies fast bowlers, who had put the hosts in an advantageous position with regular strikes.
After 40 overs, India had 210 runs on the board and only Kohli to bat with tail-enders as pace duo of Kemar Roach and Tino Best had polished off the Indian middle-order.
Kohli responded to the challenge in the best possible manner as India scored 101 runs in the last 10 overs and his contribution was 67 runs.
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R Ashwin supported Kohli well with his 18-ball 25 as they shared a 90-run stand for the seventh wicket in 8.2 overs.
Coming into the make-or-break match, both the Indian openers batted with a lot of responsibility. They chose caution over aggression, relying on rotation of the strike and hitting an odd boundary in between.
Dhawan, who by nature is a stroke-maker, kept his natural urge to go for strokes under control till India had safely negotiated almost half-the-overs.
The left-hander opened up after India had crossed 100-run mark. He chose local lad and highly-rated spinner Sunil Narine for some punishment, hitting him for two sixes and a four.
Sharma too joined him in the pavillion when he edged one behind off Tino Best. In space of seven overs India lost Suresh Raina (10), Dinesh Karthik (6) and Murali Vijay (27).
Ravindra Jadeja's run out made things worse for India but Kohli pulled India out of trouble.