The veteran duo had combined for century stands the previous two times they batted together against Sri Lanka in Test cricket and a 218-run partnership on day two ensured Pakistan were in full control.
After Younis was dismissed for 136 in the evening session, Misbah remained unbeaten on 105 at the close as Pakistan reached 327 for four and a lead of 126 runs.
Younis' 23rd Test century moved him level with Javed Miandad in Pakistan's all-time list of Test century-makers and just two behind Inzamam-ul-Haq's record mark.
By contrast it was just the fifth Test ton for the 39-year-old Misbah and the perfect reply after a 2013 in which he earned some criticism for failing to turn fifties into three figures in all formats.
Younis and Misbah had come together with Pakistan in some trouble at 83 for three after Sri Lanka were bowled out for 204 inside the opening day.
Mohammad Hafeez (11) lasted only until the fourth over of the morning session when he fell to a marvellous catch by Kaushal Silva at short cover off the bowling of Suranga Lakmal.
Debutant Ahmed Shehzad (38) then recklessly pulled Shaminda Eranga (two for 63) to Dimuth Karunaratne at backward square leg.
Misbah strode to the crease and with Younis they slowly strangled the Sri Lanka attack into submission.
Their scoring rate was at times laborious - Misbah needed 241 balls for his century - but they ushered their side into an important lead without any undue concern.
Misbah survived a tough chance on 69 when he made only fine contact with a paddled shot at Rangana Herath, but Mahela Jayawardene failed to hold on running around from slip.
Jayawardene had earlier thought he did have his man when he reviewed an lbw decision off Herath that the TV umpire Sundaram Ravi dismissed after long deliberation over a possible inside edge.
Younis showed some acceleration to complete his century just before tea - and with the new ball almost due - and cover drove Herath to the ropes to bring up the milestone up from his 147th ball.
Together with Misbah he appeared firmly entrenched until the 36-year-old finally played down the wrong line and was bowled by Eranga an hour into the evening session.
There was still time for Misbah to follow him into three figures - racing through after a fumble at mid-on - before dropping anchor for the end of the day.
With Asad Shafiq (12 not out) Misbah added just 26 in the 14 overs after Younis' exit.
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