Shakib took two wickets and scored crucial 18 (11) runs in the match while Taskin Ahmed also picked three wickets by conceding 33 runs.
Afghanistan boosted by return of Rashid Khan captain for T20I series against Bangladesh.
The 546-run win is their biggest victory margin (by runs) in Tests and third-best overall.
Star all-rounder returns to Bangladesh squad for Afghanistan ODIs.
Naveed and Abdulrahimzai have earned their maiden Afghanistan call-ups in the Hashmatullah-led squad.
Bangladesh includes two uncapped players batsman Shahadat Hossain Dipu and pacer Mushfik Hasan.
Afghanistan one-off Test against Bangladesh to be played from June 14.