Hasan's 70 off 45 balls powered Bangladesh to 139-6 in 19 overs after young off-spinner Afif Hossain spearheaded the bowling effort with 2-9, helping the home side restrict Afghanistan to 138-7 in 20 overs.
In pursuit of a modest target, Bangladesh wobbled at the start as openers Liton Das (four) and Najmul Hossain (five) both fell cheaply before Shakib put on 58 runs with Mushfiqur Rahim to steady the innings.
Mushfiqur made 26 off 25 balls, but not before he was dropped by substitute fielder Najib Tarakai off Mohammad Nabi on 14.
Medium pacer Karim Janat dismissed Mushfiqur in the 11th over before a floodlight disruption enabled Afghanistan’s bowlers to regroup.
Rashid Khan struck twice after the delay and debutant Naveen-ul-Haq also claimed a wicket as Bangladesh lost Mahmudullah (six), Sabbir Rahman (one) and Afif (two) in quick succession to slide to 104-6.
Mosaddek Hossain cut Rashid late for a brilliant boundary to ease some pressure on the home side before Shakib struck the Afghanistan skipper for a four and six in consecutive balls to take Bangladesh close.
“If you look at the last few months, we haven’t been up to the mark in T20s. We’re working on it. The bowlers bowled well on the wicket,” Shakib said after the match. “We needed someone to bat through the innings. And luckily today it was my day,” he said.