Though Bangladesh claimed two big wickets -- of overnight batters Abid Ali (91) and Shafique (73) -- midway through the morning session, they still needed a miracle to deny the tourists victory early on the fifth day. And, Babar Azam (13 not out) and Azhar Ali (24 not out) completed the formalities in the morning session to help Pakistan take a 1-0 lead in the two-Test series.
Earlier, Pakistan resumed the day on 109/0, with only 93 needed and 10 wickets in hand. After scoring just one run in the first three overs, Abid struck a boundary off Taijul Islam. In the spinner's next over, the Pakistan opener smashed him for three fours in a row with victory in clear sight.
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In the 10th over of the day, the introduction on Mehidy Hasan did the trick for Bangladesh. He scalped the wicket of Shafique, trapping him in front for 73 and breaking the productive opening partnership of 151.
But that wicket came too late for the hosts as Pakistan were just 51 runs away from victory with nine wickets still in hand. Azhar Ali joined Abid at the crease, coming in at No.3. The latter crunched a couple of boundaries and moved into the nineties but Taijul got the better off Abid's nerves as he had him trapped lbw for 91.
Abid was declared 'Player of the Match' for his contribution with the bat -- 133 and 91. Shafique, who made his Test debut, had scores of 52 and 73.
With the win, Pakistan collected 12 World Test Championship points and jumped to the second spot on the table.
The second Test will be played in Dhaka from December 4.
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Brief scores: Bangladesh 330 and 157 all out lost to Pakistan 286 all out and 203 for 2 in 58.3 overs (Abid Ali 91, Abdullah Shafique 73, Azhar Ali 24 not out).