India were put into bat first and made 178-4 before England posted a score of 158-6 from their 20 overs.
However, a unbeaten knock of 74 from Virat Kohli and Suresh Raina's 54 saw India surge towards a competitive total. MS Dhoni then chipped in with 21 not out at the end of the innings to put his team in a commanding position in the match.
Michael Lumb (36), Moeen Ali (46) and Jos Buttler (30) gave England a steady footing in the contest when it was their turn to bat, but disappointing scores from Alex Hales (14), Eoin Morgan (16), Bopara (6) saw them come up short.
England's World T20 campaign gets underway on Saturday when they take on New Zealand in Chittagong.