Shafali and stand-in skipper Smriti Mandhana (47 off 38 balls) added 96 for the opening stand while Jemimah and Deepti Sharma (10) added 29 runs in just 2.3 overs.
The Indian bowlers then defended the target easily, restricting the hosts to 100 for 7.
Captain Nigar Sultana top-scored with 36 while Fargana Hoque made 30.
For India, Shafali Verma and Deepti Sharma picked up two wickets apiece.
Brief Scores: India 159 for 5 in 20 overs (Shafali Verma 55, Jemimah Rodriguees 35 not out; Rumana Ahmed 3/27) vs Bangladesh 100 for 7 in 20 overs (Nigar Sultana 36; Shafali Verma 2/10, Deepti Sharma 2/13).