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.
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 today.
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 has so far hit 13 boundaries and four sixes. Imrul has 15 fours and three sixes.
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