The experienced pair of Mithali Raj (49 not out) and Smriti Mandhana (41) put up a 70-run stand for the opening wicket to take India to 118 for six in 20 overs.
The team led by Harmanpreet Kaur was clinical with the ball, bowling out Bangladesh for a mere 54 runs for a comprehensive victory.
The star bowler for India was leggie Poonam Yadav, who picked up three wickets and conceded just 13 runs in four overs.
India, whose participation in the tournament was under cloud due to the presence of arch-rivals Pakistan, next play hosts Thailand tomorrow.
It remains to be seen whether they face Pakistan on November 29. Both teams are scheduled to play the exciting clash, according to the Asian Cricket Council website.
The Indians, however, go into their game against Thailand high on confidence with the result today.
Raj, who was removed as T20 captain prior to the tournament, proved why she still has a lot to offer in the shortest format.
She remained unbeaten right till the end and just two boundaries in her 59 ball knock showed how hard she had to work for every run.
India should have set a bigger total, especially with the kind of start provided by the openers. However, that wasn't to be as they lost their way in the second half of the innings.
In the other match of the day, Pakistan too began their campaign on an emphatic note by giving Nepal a nine wicket thrashing.
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