Kohli's magnificent 55 not out was the difference between the sides in the rain-hit 18-overs-a-side match, coming under tremendous pressure on a prodigiously turning track at Eden Gardens.
Chasing 119 to secure their first win of the tournament, India slumped to 23-3 in the fifth over before Kohli and Yuvraj Singh (24) shared a match-high 61-run partnership to virtually take the game away from Pakistan.
Home captain Mahendra Singh Dhoni smashed a six to level the scores and took a single to seal victory with 13 balls to spare as India bounced back from their shock opening defeat by New Zealand.
Kohli made batting look ridiculously easy on a difficult track, embellishing his unbeaten 37-ball knock with seven fours and a six, and he was the obvious choice for the man-of-the-match award.
Pakistan, put into bat, found the going difficult, especially against India's slow bowlers as they scored 118-5.
Openers Sharjeel Khan (17) and Ahmed Shehzad (25) were subdued by the Indian bowlers and Shahid Afridi could not justify his promotion to number three.
Shoaib Malik (26) and Umar Akmal (22) added 41 runs in four overs to take Pakistan past the 100-mark to ensure their pace-heavy attack had something to defend.
The match between the winners of the first two editions of the tournament was originally scheduled in the picturesque north Indian city of Dharamsala before Pakistan's security fears led to it being moved to Kolkata. – Reuters
Original source: #WT20 Kohli steers India to victory