Skipper Bismah Maroof and opening batter Javeria Khan were at the helm of Pakistan's strong batting performance.
The duo stitched a 95-run stand laced with boundaries for the second wicket, helping Pakistan post an imposing total of 167-3 in their 20 overs.
Sidra Ameen fell inside the Powerplay to Jahanara Alam, who picked up four wickets in the preceding game between the two sides.
Bismah and Javeria then steadily kept the scoreboard ticking with their nifty strokeplay piercing the gaps while occasionally opting for the aerial route.
The wickets of Javeria for a sublime 44-ball 52 and Iram Javed towards the end of the innings threatened to halt Pakistan's progress but Bismah held one end firmly and tactfully upped the scoring rate.
Bangladesh's hopes of restricting the opposition to a sub-150 total diminished as Bismah and Aliya Riaz added 24 runs in the final two overs.
The tourists were rocked by early strikes including the dismissal of Rumana Ahmed following miscommunication with her batting partner Sanjida Islam.
Rumana, who smashed a 30-ball 50 in her side's defeat in the last match, fell short of the popping crease and had to make her way back to the pavilion with Bangladesh struggling at 25-3.
Sadia Iqbal then accounted for the prized scalp of Sanjida after her solid 57-run partnership with Nigar Sultana Joty revived Bangladesh's chances of chasing down the challenging target.
Sadia went on to claim two more wickets while veteran off-spinner Sana Mir chipped in with the wicket of the dangerous Fargana Hoque.
A couple of maximums from Jahanara in the death overs did little to help the visitors' cause as the asking rate exceeded their grasp.
Bangladesh stuttered to 152-7 allowing the jubilant Pakistan team to celebrate their series win at home.
Bismah's 50-ball 70 glittered by nine boundaries and a solitary six saw her grab the player of the match award.
Pakistan are now well-placed to complete a series whitewash over their Asian rivals as the final game will take place at the same venue on Wednesday.