Opener Shehzad led from the front for Pakistan, who won the toss and chose to bat in Dhaka.
The 22-year-old finished on 111 not out from just 62 balls as batting partners came and went. Pakistan finished their 20 overs on 190-5, thanks to a late flourish from Shahid Afridi.
Bangladesh have now lost 40 matches in a row against Pakistan. They scored solidly enough in their reply but never really threatened to reach the 191-run win total.
They finished on 140-7, with Shakib Al Hasan top-scoring with 38 runs from 32 balls.
Pakistan's victory means that whoever win their final group game against the West Indies will join India in the semi-finals. Meanwhile, Australia are knocked out of the tournament.