The match ended in the extended opening session of the fourth day after a Taskin bouncer hit Zahir Khan, forcing the final batsman to retire hurt.
The visitors barely made a dent in their mammoth case of 662, giving the hosts the biggest Test win by runs since Australia's 562-run victory over England in 1934.
It was more than double Bangladesh's previous record of 226 wins over Zimbabwe at Chittagong in 2005. The home side's triumph was all but guaranteed after they declared their second innings at 425-4 in Friday's final session.
Afghanistan stumbled quickly, losing Ibrahim Zadran for a duck off the first ball of the innings and resuming on Saturday at a precarious 45-2.
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