Younus hit 136 for his 23rd hundred while Misbah was 105 not out for his fifth as Pakistan reached 327 for four 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 Younus and Misbah sharing 218 runs for the fourth wicket.
Younus hit spinner Rangana Herath for his 13th boundary to complete his hundred, taking just 47 balls for his second 50 runs. He also hit a six.
Younus equalled Javed Miandad's record of 23 centuries, the third highest for Pakistan in the list topped by Inzamamul Haq (25) and Mohammad Yousuf (24).
Younus 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.
Misbah had also survived a close leg-before appeal on 48 off a luckless Herath as Sri Lanka's referral was wasted as TV umpire Ravi Sundaram adjudged the ball had hit the bat.
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.
Sri Lanka had taken the second new ball with Pakistan 251 for three but they only bagged one wicket in the last two sessions.
Eranga was the best bowler with two off 63.
The second Test will be played in Dubai (January 8-12) and the third in Sharjah (January 16-20).
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Younus and Misbah are by far the two best test batsman from the current lot in the Pakistani squad. Great technique and tons of patience.