Cremer claimed four wickets with his leg-spin to trigger a Bangladesh collapse as the hosts slipped from 147-2 to 170- 8. Paceman Kyle Jarvis took three wickets.
Bangladesh opener Tamim Iqbal top-scored with 76, providing a strong start with a 106-run second wicket partnership with Shakib Al Hasan, who made 51, after electing to bat first.
It was Tamim's third successive half-century in as many matches of the tournament. The left-handed batsman also became the first Bangladeshi to amass 6,000 ODI runs during his 105- ball stay.
Zimbabwe would join Bangladesh in the final on Saturday if they can win the contest.
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