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Captain Mithali Raj made 42 off 35 balls, Harmanpreet Kaur 40 from 29 and Vellaswamy Vanitha 38 off 24 in India's 163-5 in Bangalore.
Anuja Patil claimed 2-16 and Poonam Yadav 2-17 as Bangladesh managed only 91-5 en route to their second heaviest T20 defeat in terms of runs.
New Zealand, twice runners-up, opened their campaign with a seven-wicket win over Sri Lanka in Delhi.
Sri Lanka were well placed when Dilani Manodara and Yasoda Mendis shared 53 for the second wicket, but slipped from 81-2 in the 13th over to 110-8.
New Zealand raced to their target with 25 balls to spare, captain Suzie Bates making 37 at a run a ball and Sara McGlashan ending unbeaten on 21 from 14 deliveries.
England, winners in 2009, face Bangladesh at 10:00 GMT on Thursday.
India opened the Women's World Twenty20 with a 72-run victory over Bangladesh.