The pair batted through the afternoon session of the opening day to put on an unbroken stand of 84 for the fourth wicket and steer the tourists from a shaky 56-3 to 140-3 by tea.
Khan, playing his 90th Test, returned unbeaten on 77 with five boundaries and a six. Misbah was on a typically dour 22 off 87 balls.
Khan was reprieved by the Decision Review System (DRS) when he was on 59 after umpire Bruce Oxenford had declared him leg-before to off-spinner Dilruwan Perera.
The partnership between Pakistan's two elder statesmen came after the morning session belonged to Sri Lanka with three quick wickets in the bag.
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Seamer Dhammika Prasad removed both openers cheaply to make it 19-2 by the sixth over before a partial recovery helped the tourists move to 59-3 by lunch.
Prasad, working up a tidy pace on a pitch that afforded bounce and movement, bowled Ahmed Shehzad off the inside edge with his third delivery after being hit for a boundary off the first.
The seamer then trapped Khurram Manzoor leg-before in his third over, but Azhar Ali and Khan settled in to put on 37 as the wicket eased out under the mild sun.