The all-rounder took her team to a resounding seven-wicket win with an unbeaten 42 and three wickets in Kuala Lumpur on Wednesday.
Salma Khatun and Co restricted India to 141 by giving away only 20 runs in the last four overs and then finished the chase with two balls in hand.
The two teams have faced each other 10 T20s and four One-Day Internationals.
This is also the first-ever Asia Cup defeat for India, who have taken home the titles of all six editions of the tournament.
The 142 total against India is also the highest posted by Bangladesh Women in T20.
Fargana Hoque accompanied Player of the Match Rumana to the victory with an unbeaten half-century after opener Shamima Sultana left a strong base with 33 - something she did against Pakistan.
Fargana and Rumana now hold the record partnership of 93 runs for Bangladesh.
India Captain Harmanpreet Kaur contributed highest 42 to their total after she won the toss and chose to bat first.