Hosts India got their World Twenty20 campaign back on track after beating arch rivals Pakistan on Saturday.
More than 60,000 fans packed into Eden Gardens in Kolkata to watch the highly-anticipated game.
Pakistan got off to a sluggish start on a difficult wicket but thanks to Shoaib Malik and Umar Akmal set a target of 118-5.
After Pakistan bowled Shikhar Dhawan and Suresh Raina, Virat Kohli took over for India and his unbeaten 55 proved crucial as the home side reached their target of 119 with three overs spare.
MS Dhoni hit the winning runs for the host nation who are now third in Group 2 behind leaders New Zealand and Pakistan with their next match against Bangladesh in Bangalore on Wednesday.