Pakistan enter the competition at the top of group 2, and could leave their rivals on the brink of elimination if they overcome India on Saturday.
Shaid Afridi's men built a total of 201-5 as they fielded first.
Mohammad Hafeez and Ahmed Shehzad both made brisk fifties in a stand of 95, before their captain added to the score with 49 from 19 balls.
Bangladesh responded with 146-6, but Afridi and Mohammad Amir claimed two wickets each for Pakistan.
23 year-old Amir fired past the defences of Soumya Sarkar with his third delivery, and caught out Mushfiqur Rahim later in the innings with a slow ball.
The match marked his return to the world stage after a five-year ban for spot-fixing five years ago.
Pakistan’s captain then took centre-stage, outplaying Sabbir Rahman with a leg-spin before claiming his 37th Twenty20 wicket from Tamim Iqbal.
In recent years, Afridi has lacked efficiency in the sport’s shortest format, as he boasts just 17 runs and three wickets in his past six Twenty20 internationals.
But the all-rounder answered critics in emphatic fashion in Kolkata, with both the bat and the ball.
As Pakistan were already cruising to victory at 121-2 and 6.1 overs remaining, the 37 year-old delivered the final blow to Bengladesh with four fours and four sixes.
"My performances play a key role, but I was hungry", he said after the match.
"I was keen to perform well for my country in this event. It's a big event as captain, as senior player, I had to lead by example."
After a strong performance at the Asia Cup, the Tigers were hopeful ahead of the Wednesday's match. But with Pakistan's bowling attack and after six overs, a recovery seemed almost impossible.
"You can't practice much, you have to be mentally strong", said Bangladesh captain Mashrafe Mortaza, before turning to his team's next match against Australia in Bagalore on Monday.
"With Australia's batting, it will be hard and Bangalore wicket will be flat. The bowling group must bring better plans."