Asked to bat first in Colombo, Sri Lanka on Friday, Bangladesh posted 155 runs for eight wickets in their stipulated 50 overs with Fargana Hoque top-scoring with a 107-ball 50. Opening batter Sharmin Akhter scored 35 off 82 deliveries.
Seamer Mansi Joshi bagged three wickets while Devika Vaidya picked up two.
In reply, India chased down the target in 33.3 overs with opener Mona Meshram scoring the highest, unbeaten 78. Captain Mithali Raj was also undefeated on 73.
Earlier, Pakistan and South Africa had progressed to the Super Six, alongside Bangladesh, from Group B.
Meanwhile in Group A, India, Sri Lanka and Ireland went through to the Super Six. Among these six teams, the top four sides will qualify for the World Cup, scheduled to be held in England in June.
Bangladesh began their Super Six campaign by beating Ireland by seven wickets on Wednesday. They will face host Sri Lanka in their last Super Six game this Sunday.
Australia, New Zealand, host England and the West Indies have already qualified for the World Cup as the top ranked teams.
158/1 in 33.3 overs (Meshram 78*, Mithali 73*, Kubra 1/37) beat Bangladesh women
155/8 (Fargana 50, Sharmin 35, Joshi 3/25) by nine wickets