Bangladesh slipped from 128 for 4 to 136 for 9 before a last-wicket stand took them through.
Star all-rounder returns as Bangladesh announce their 16-member squad for ODI series against India.
Pakistan clinch a semi-final spot at the ICC T20 World Cup with a five-wicket victory over Bangladesh in Adelaide on Sunday.
Arshdeep, Hardik fashion crucial win despite Litton Das (27-ball, 60) special.
BCB announced Team India would tour their country in December this year.
Bangladesh surge late to set Zimbabwe a tough chase.
