Younis furthered his third consecutive century in as many innings and was unbeaten on 141 and with him skipper Misbah-ul Haq on an aggressive 55 as Pakistan continued to bat solidly against a hapless Australian attack.
That raised Pakistan's chances of winning their first series against Australia in 20 years after they won the first Test by 221 runs in Dubai.
Younis added another 73 runs for the fourth wicket with Misbah after Pakistan resumed at 304-2 and added 101 in an extended two-and-a-half hours session due to Friday prayers.
Younis has so far hit eleven boundaries and a six during his 244-ball knock.
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Australia had another unusual sloppy day in the field as David Warner failed to hold a sharp chance at point from Younis's push off paceman Mitchell Johnson in the third over of the day. Younis was then batting on 112.
Nine runs later Younis edged a Peter Siddle delivery which fell short of Brad Haddin who hurt his right shoulder in an attempt to hold the catch.
But Warner made amends as he took a good catch off Ali's glance off paceman Mitchell Starc for a consolation wicket.
Ali's 250-ball knock had six boundaries.
Misbah, playing his 50th Test, took the attack to the Australian bowlers with a second-ball six off Lyon and reached his 27th half-century with his sixth boundary, taking just 76 balls.