Younis, who came in to bat at 19-2 on the first morning, anchored the innings admirably to enable the tourists to pile up 451 all out by tea on the second day.
Sri Lanka replied with 99 for one by close, comfortably tackling both pace and spin, but the batsmen will remain wary of the turn and bounce that will increasingly come into play over the next three days.
Left-arm seamer Junaid Khan trapped Upul Tharanga leg-before for 19 in the fifth over but Kaushal Silva and Kumar Sangakkara settled in to put on 75 for the second wicket.
The 36-year-old Younis, who is playing his 90th Test, batted for eight hours and 16 minutes, hitting 15 boundaries and a six in his 24th Test century.
Pakistan, who resumed at their overnight score of 261-4, went to lunch on 347-5 with Asad Shafiq making 75 during a fifth-wicket stand of 137 with Younis.
The visitors added 32 runs in the first hour when left-arm spinner Rangana Herath broke through for Sri Lanka by trapping Shafiq leg-before. The batsman's appeal to the TV umpire went in vain.
Off-spinner Dilruwan Perera, who had gone without a wicket for four sessions, struck five times in the post-lunch period to hasten the end of Pakistan's innings.
Perera ended Khan's vigil soon after lunch by beating the well-set batsman in the air, resulting in an easy catch at short mid-wicket, a soft dismissal that came against the run of play.
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