Haque (80) put on 95 for the third wicket with Mahmudullah (49) after opener Kayes (51) had batted resolutely at the start of the day, and the Tigers reached 236-4 at stumps in Khulna after Haque departed from the final ball of the day.
However, Pakistan shelled a numbers of catches at the Sheikh Abu Naser Stadium, with Zulfiqar Babar’s caught-and-bowled drop of Haque when the Bangladesh batsman was on 17 perhaps the most costly.
The hosts – fresh from whitewashing Pakistan 3-0 in their recent one-day series and also winning the solitary Twenty20 International – scored slowly early on after electing to bat.
Kayes and Tamim Iqbal (25) brought up their fifty partnership in the 27th over, though Tamim – who scored two hundreds in the ODI showdowns with Pakistan – was the beneficiary of a drop by Mohammad Hafeez at leg slip.
Tamim eventually edged spinner Yasir Shah to short leg around 10 minutes before lunch and was given out after third umpire Paul Reiffel decided the bowler had got enough of his foot behind the line.
Bangladesh played more aggressively after the interval with Kayes and Haque adding 40 for the second wicket before the former was dismissed by Hafeez, the spinner’s first wicket with his re-modelled action.
But Haque found a good ally in Mahmudullah, who played an array of attractive strokes prior to edging left-armer Wahab Riaz behind to Sarfraz Ahmed in the 74th over, the wicketkeeper taking a superb one-handed catch.
Shakib Al-Hasan (19no) joined forces with Haque at the point and the pair added 49 for the fourth wicket before Haque was trapped lbw by Babar in the final piece of action.
Bangladesh had earlier handed Test-match debuts to all-rounder Soumya Sarkar and paceman Mohammad Shahid, while Pakistan did the same to teenage left-handed batsmen Sami Aslam as well choosing to leave out Saeed Ajmal.