Bangladesh lost their opener Murshida Khatun cheaply before Sharmin Akhter steadied the side with Fargana, putting on 70-run for the second wicket stand.
Sharmin scored 31 before being dismissed. Her dismissal led a mini collapse as the Pakistan bowler came back strongly to make regular intervals. Rumana however remained cool under pressure and eventually delivered the victory.
Rumana also scalped 1-40 in bowling after Pakistan were put into bat first. Bangladesh had wobbled them at 49-5 at the very outset with Nahida Akhter and Ritu Moni scything down the top and middle order.
But the resistance came from Nida Dar and Aliya Riaz who combined for 137-run for the sixth wicket stand to help Pakistan go past 200 runs mark. Nida clubbed eight boundaries and two sixes for her 111 ball-87 while Aliya was unbeaten after hitting 61 off 82 with four fours and two sixes.
Ritu Moni and Nahid claimed two wickets apiece while Salma and Ruman picked up one wicket each.
Three spots up for grabs for the ODI World Cup scheduled for next March-April in New Zealand from this qualifier.