Younis was unbeaten on 103 for his 23rd hundred and Misbah was 74 not out as Pakistan reached 251-3 at tea in reply to Sri Lanka's first innings total of 204.
Pakistan now lead by 47 runs and with Younis and Misbah sharing 168 for the unbroken fourth wicket stand, Pakistan look for a match-winning edge.
Younis hit spinner Rangana Herath for his 13th boundary to complete his hundred, taking just 47 balls for his second fifty runs. He has also hit 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 has so far hit ten boundaries during his 164-ball knock.
Hafeez had started off well, hitting two straight boundaries off Lakmal before miscuing a drive off the same bowler and was smartly caught at short cover by Kaushal Silva.
Silva, also a wicket-keeper but selected as opener in this Test, dived to his left and caught the ball inches from the ground.
Shehzad also miscued a hook shot and was caught at forward square-leg by Dimuth Karunaratne after hitting three boundaries.
The second Test will be played in Dubai (January 8-12) and the third in Sharjah (January 16-20).
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