Resuming on 318 for four, Sri Lanka were all out for 388 in their first innings in the morning, losing their last six wickets for 68 runs.
Pakistan's second innings started abysmally as left-arm spinner Rangana Herath dismissed opener Ahmed Shehzad at the stroke of lunch and paceman Nuwan Pradeep struck twice early in the afternoon to reduce them to 19 for three.
That brought Younus, who completed his 28th half century in tests, and captain Misbah together and the pair went about carefully in their rescue mission.
Misbah was lucky to survive a couple of run-out chances but looked solid on the way to his 23rd test fifty.
Earlier, Angelo Mathews (42), who was dropped by wicketkeeper Sarfraz Ahmed off Rahat Ali on Thursday evening, edged a similar delivery from the same bowler in the morning.
Sarfraz made no mistake this time, diving to complete the catch, and the Sri Lanka captain departed without adding to his overnight score after a 93-run stand with Mahela Jayawardene.
Jayawardene, running out of partners, went for some quick runs and was bowled on 129, trying to play a reverse sweep against Saeed Ajmal.
During the course of his innings, the stylish right-hander passed Australian Steve Waugh to move to number eight on the list of highest run-scorers in tests. Waugh had scored 10,927 runs, while Jayawardene's tally stands at 10,940.
(Writing by Sudipto Ganguly,; editing by Pritha Sarkar)
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