Younis hit 136 for his 23rd hundred while Misbah was 105 not out for his fifth as Pakistan reached 327-4 at the close on the second day in reply to Sri Lanka's first innings total of 204.
Asad Shafiq was the other not out batsman with 12 as Pakistan dominated the day after Sri Lanka took two early wickets in the first session.
Pakistan now lead by a healthy 123 runs, primarily because of Younis and Misbah sharing 218 runs for the fourth wicket.
Younis equalled Javed Miandad's record of 23 centuries, the third highest for Pakistan in the list topped by Inzamam-ul Haq (25) and Mohammad Yousuf (24).
Younis was finally bowled by paceman Shaminda Eranga after his 198-ball knock which included 19 fours and a six.
Misbah had luck on his side as he was dropped by Mahela Jayawardene when on 69, as he tried to paddle sweep Herath and the fielder, moving to leg-slip, failed to hold an easy chance.
The Pakistani skipper reached his hundred with a single off spinner Sachitra Senanayake, taking 297 minutes for the century which included 12 boundaries.
He has so far hit 13 boundaries in his chancy innings and once again proved to be the mainstay for Pakistan.
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