The win saw England stay alive with a chance to qualify for the semi-final stages.
At one stage it looked that England might score 350+ runs on the board before Mohammed Shami's five-for pegged them back to claim his maiden WC five-wickets haul.
The speedster became the second Indian after Narendra Hirwani (in 1988) to claim three four-wicket hauls in successive matches. He also became the 2nd bowler after Shahid Afridi to do so in World Cup games.
The stage was all set for experienced batsman MS Dhoni and 'hard hitter' Hardik Pandya to see India home, but an attempt to hit Plunkett out of the park saw Pandya (45) dismissed in the 45th over with India still needing another 71 runs off 31 balls.
Kedar Jadhav walked in to join Dhoni in the middle, but the England bowlers kept bowling a tight line as the duo failed to score at around 15 runs every over. While Dhoni finished with an unbeaten 31-ball 42, Kedar was unbeaten on 12 off 31 balls.