Nabi hit an unbeaten 84 off 54 balls under pressure to guide Afghanistan to 164-6 before Mujeeb claimed a career best 4-15 to help his side dismiss Bangladesh for 139 in 19.5 overs for their world record 12 successive Twenty20 international win.
Shah made 102 and put on a crucial 120-run fourth-wicket stand with Asghar Afghan, batting on 88, to counter the Bangladesh spin attack at the Zahur Ahmed Chowdhury Stadium in Chittagong.
Batsman Rahmat Shah on Thursday became the first Afghanistan cricketer to score a Test century, helping the minnows start strongly against Bangladesh on the opening day of the one-off match.
Rashid Khan claimed 6-49 and completed his maiden 10-wicket haul in Test cricket as Afghanistan overcame rain and fading light to crush Bangladesh by 224 runs in the one-off Test in Chittagong on Monday.
New Zealand made 173 for five off 17.5 overs after losing the toss and batting, before the weather ended their innings prematurely. As a result, Bangladesh's run chase was set at 170 from 16 overs under the Duckworth-Lewis-Stern formula.
Mayers' innings is the highest individual collection for West Indies in the fourth innings of a Test since Brian Lara stunned Australia with 153 runs in Bridgetown in 1999. "It's a great feeling to be playing Test cricket, and then going on to score 100, 200 and then to win the match," Mayers said.
The 33-year-old sparked a social media storm in the Muslim-majority nation after attending a ceremony in Kolkata dedicated to a Hindu goddess on Nov.12.
Former Bangladesh Cricket Board (BCB) president Saber Hossain Chowdhury, a British-educated lawyer, businessman and now member of parliament, said corruption was deep-rooted at the governing body.
Bangladesh's professional cricketers − including several members of the national squad − went on strike on Monday to call for better pay and benefits.