Bangladesh captain Najmul Hossain Shanto’s century and 91 from Mominul Haque led the hosts to score 413 in their first innings.
Pakistan opener Azan Awais, 21, hit a century on his Test debut as the tourists made 386 in reply, a deficit of 27 runs.
After significant rain interruptions on days three and four, the Tigers declared on 240-9 – Shanto (87) and Monimul (56) again starring – before lunch on the final day to try and set up a push for victory.
Abdullah Fazal made a defiant 66 but did not receive enough support as Pakistan failed to bat out the day for a draw, with Taskin Ahmed and Taijul Islam picking up two wickets each.
“Very happy,” said Tigers captain Shanto. “Proud of all the guys the way we played.
“We declared because we have a quality bowling attack and in these conditions Rana, Taskin, Taijul bowled really well and that’s what I want from them.”
The second and final Test starts in Sylhet on Saturday.
