The left-handed pair put on their nation’s highest partnership for any wicket as Bangladesh, trailing by 296 runs on the first innings, closed the day strongly at 273 for no loss in their second knock.
Tamim was unbeaten on 138 to become the first Bangladesh batsman to score seven Test centuries. He beat former captain Mohammad Ashraful’s tally of six hundreds.
It was Tamim’s third century in as many Tests, having made identical scores of 109 in the last two matches against Zimbabwe in November.
Imrul scored 132 not out, his third hundred, as the bowlers toiled on the placid wicket at the Sheikh Abu Naser stadium that has already produced 1,233 runs and just 20 wickets over the four days.
The pair batted through just over two sessions to surpass the previous Bangladesh record of 267 by Ashraful and current skipper Mushfiqur Rahim for the fifth wicket against Sri Lanka in Galle in 2013.
Tamim and Imrul had put on an opening stand of 224 during Bangladesh’s previous Test — against Zimbabwe in Chittagong — and carried on in the same manner on Friday.
Fears that Bangladesh may struggle to bat out two days to save the match, after Pakistan ran up 628 in their first innings, proved unfounded as the openers settled in to tame the bowling.
Tamim reached his century after tea with two consecutive boundaries off Junaid Khan. Imrul swept Zulfiqar Babar for a single soon after to bring up his own landmark in front of some 5,000 delighted home fans.
Tamim has so far hit 13 boundaries and four sixes. Imrul has 15 fours and three sixes.
Earlier, the tourists took their overnight score of 537 for five to 628 before they were all out shortly before lunch.
The overnight pair of Asad Shafiq (83) and Sarfraz Ahmed (82) carried their sixth-wicket partnership to 126 to build a sizeable lead for Pakistan.
Left-arm spinner Taijul Islam picked up three of the five wickets in the morning session to finish with creditable figures of six for 163.
Debutant fast bowler Mohammad Shahid claimed his first Test wicket when he ended the sixth-wicket stand by having Sarfraz caught at mid-on by substitute fielder Litton Das.
Taijul bowled Wahab Riaz for zero in the next over and then trapped Yasir Shah leg-before that gave the 23-year-old his third five-wicket haul in six Tests so far.
Between those two wickets, star all-rounder Shakib Al Hasan claimed his lone success in the innings when he took a return catch to dismiss Shafiq.
Tajiul wrapped up the innings when wicket-keeper Mohammad Mahmudullah, standing in for the injured Rahim, stumped Zulfiqar Babar.
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