After winning the toss and opting to bat on Saturday, India set the tone early on as Sanju Samson (111) and skipper Suryakumar Yadav (75) left Bangladesh reeling with an explosive 173-run partnership off just 70 balls.
Samson, in particular, was exceptional, bringing up his maiden T20I century in just 47 balls, the second-quickest century in the shortest format by an Indian - second only to Rohit Sharma's 35-ball century against Sri Lanka in 2017.
Tanzim Hasan Sakib had a tough day with the ball, conceding 66 runs, the most by a Bangladesh bowler in a T20I innings, surpassing Rubel Hossain's previous unwanted record of 63 runs.
India's total was the highest by a full ICC member and only surpassed by Nepal's 314 against Mongolia last year.
India spinner Ravi Bishnoi delivered an impressive spell, taking 3-30 in his four overs to stifle Bangladesh's middle order, while fast bowler Mayank Yadav took two wickets.
Bangladesh batsmen Towhid Hridoy (63no) and Litton Das (42) provided some resistance, combining for 53 runs, but their teammates failed to offer substantial support, as India's disciplined bowling and fielding restricted them to 7-164 in their 20 overs.
Samson has struggled for form since the T20I series in Sri Lanka in July, where he was dismissed for two consecutive ducks while his performances in the first two games of the series against Bangladesh were also underwhelming.
"I have also felt I can do much better but with playing so many games I know how do deal with pressure and my failures because I have failed a lot," Samson said, reflecting on his previous struggles.
"I wanted to perform and wanted to show. The leadership tells me they back me no matter what... not just in words but in actions also. Last series I got two ducks and went back to Kerala thinking what will happen, but I'm here."
Captain Yadav added: "I think we've achieved a lot as a team. We said we wanted to have selfless cricketers and want to be a selfless team, enjoy each others' performances and that camaraderie is coming off."
