Electing to bat, Bangladesh could manage a paltry 88 for four in 20 overs, which the Indians comfortably overhauled with two overs to spare.
Openers Anagha Deshpande (28) and Mona Meshram (29) put together a steady 52-run stand in 10.3 overs.
After that skipper Harmanpreet Kaur (11) and Poonam Raut (18) shared an unbeaten 28-run stand to take India past the finishing line with ease. The hosts, though, lost three wickets in quick succession.
Earlier, the Indian bowlers were on the money from the onset, denying the Bangladeshi openers to free their arms.
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Shahanaz Parvin (15) and Farzana Haque (23) made a slow start, adding just 30 runs in 9.3 overs for the opening wicket.
Shukhtara Rahman, however, tried to give impetus to the Bangladesh innings, taking on the Indian bowlers by hitting two sixes in her brief 25-ball 27-run knock. Skipper Salma Khatun remained unbeaten on 16.
Pacer N Niranjana (1/14) and left-arm spiner Ekta Bist (1/11) grabbed a wicket each while two batswomen were run out.
India Women 91 for three in 18 overs (Mona Meshram 29, Anagha Deshpande 28; Panna Ghosh 2/18).