Shocked by New Zealand in their opening match, when they failed to chase 127 in Nagpur, the hosts kick-started their campaign by reeling in a victory target of 119 which maintained their unbeaten record against Pakistan in 50-over World Cups and World T20s.
The did not have it all their own way though, slipping to 23 for three after the five-over powerplay, but a 61-run partnership between Kohli and Yuvraj Singh got their side back on track.
Despite Yuvraj departing for 24, Kohli steered India home with an unbeaten 55 from 37 deliveries to enhance their chances of qualifying from Group 2 with games against Australia and Bangladesh still to come.
The Super-10 match, switched from Dharamsala due to security concerns, was reduced to 18 overs per side after rain delayed the start by an hour.
India skipper Mahendra Singh Dhoni won the toss and opted to chase, his bowlers restricting Pakistan to 118 for five on a pitch that turned sharply from the off.
Pakistan struggled for fluency until Umar Akmal and Shoaib Malik joined forces in the 12th over, the fourth-wicket pair upping the tempo with a stand of 41 in 24 balls.
Sharjeel Khan and Ahmed Shehzad operated cautiously, adding 38 in 7.4 overs until the former mis-timed a pull off Suresh Raina’s fourth ball and was well caught by a diving Hardik Pandya at mid-on.
Shehzad, having passed 1,000 T20I runs, sliced Jasprit Bumrah to point to depart for 25 and Shahid Afridi, promoted to number three, holed out in the deep off Pandya to leave Pakistan 60 for three.
But Malik struck 26 from 16 balls, the same amount of deliveries it took Umar to make 22, and the pair both showed intent by crashing the only sixes of the innings in the 14th over, bowled by Pandya.
They departed in the space of four balls, Umar edging Ravindra Jadeja behind before Malik top-edged Ashish Nehra to short fine-leg.
India’s chase got off to a poor start as after Rohit Sharma skied Mohammad Amir to cover, Shikhar Dhawan and Raina played on to consecutive Mohammad Sami balls.
Yuvraj survived the hat-trick delivery and then combined effectively with Kohli, the duo playing themselves in for five overs before starting to cut loose.
Kohli swept Malik for four and six in the 11th but after Yuvraj pulled Wahab Riaz for a maximum, he holed out in the deep attempting to repeat the shot.
Like he did against Pakistan in the recent Asia Cup, Kohli held the innings together and Dhoni smacked a six and then the winning single to complete victory with 13 balls to spare.