The match was in the balance with three overs to go, then Shadab Khan and Mohammad Nawaz hit two sixes each and Pakistan reached 132-6 in 19.2 overs, knocking off Bangladesh's 127-7.
Pakistan's ODI and Test matches against Bangladesh, which were scheduled in April, have been postponed.
Pakistan Cricket Board CEO Wasim Khan told the media that nothing has been decided on the tour by the Bangladesh team later this month.
The ODI was originally planned for April 3 in Karachi, but will now be held on April 1 at the same venue with the Bangladesh team now scheduled to arrive on March 29 in Karachi.
With the promotion up the ladder in the rankings chart, Babar is the only batsman to feature in the top five across formats - top-ranked in T20Is and No.3 in ODIs.
Bangladesh bowler Abu Jayed has been reprimanded for his aggressive celebration after dismissing Pakistan's Azhar Ali during 1st Test.
Pakistan registered a dominating victory over Bangladesh in the first Test to take a 1-0 lead in the two-match series.
PCB Chief Executive Officer Wasim Khan said that the Board was keen to have the second match as Day/Night Test and it was awaiting a response from Bangladesh.
The 16-year-old Naseem, who took 4-26, dismissed Najmul Hossain Shanto (38), nightwatchman Taijul Islam (0) and Mahmudullah (0) as Bangladesh limped to 126-6 at stumps on the third day.
Pakistan pacer Naseem Shah on Sunday become the youngest bowler ever to take a Test hat-trick and the first from his nation since Mohammed Sami in 2002.
Pakistan continued their domination in their first Test against Bangladesh, finishing Day 2 on 342/3 with a lead of 109 runs. Opener Shan Masood scored his third Test ton while Babar Azam was unbeaten on 143.
The first Test between Pakistan and Bangladesh will be played from February 7 at Pindi Cricket Stadium in Rawalpindi.
Mustafizur Rahman was named in the squad for the two-Test series in India in November but did not play in either of the Tests because of his poor form.
Bangladesh has split the tour to Pakistan into three phases due to security concerns. In the first phase it lost the three-match Twenty20 series 2-0 in Lahore with the final game abandoned due to rain last month.
The first Test between Pakistan and Bangladesh will be played in Rawalpindi from February 7-11.
Pakistan clinched the series 2-0 after beating Bangladesh by five wickets and nine wickets, respectively.
Pakistan vs Bangladesh 3rd T20I: Here are the details of When and Where to watch PAK vs BAN live cricket match online on SonyLiv.
Babar Azam and Mohammad Hafeez hit fifties as Pakistan beat Bangladesh by 9 wickets to take 2-0 lead in three-match T20I series.
Live Cricket Streaming Pakistan vs Bangladesh, 2nd T20I: Here are the details of When and Where to Watch PAK vs BAN stream live cricket match online on SonyLIV and TV Telecast on Sony ESPN.
Shoaib Malik scored a 58 not out on Friday against Bangladesh at the Gaddafi Stadium in the first T20I of the three-match series.
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