At the break, Younis was not out on 205 for his fifth double ton and with him Asad Shafiq not out on one as Pakistan reached 517-4 at tea on a flat Sheikh Zayed Stadium pitch.
Younis hit Glenn Maxwell for a towering six and in the spinner’s next over took a single to complete 200.
He has so far hit 14 boundaries and two sixes during his dominating 344-ball knock.
When on 181, Younis completed 8,000 runs in his 93rd Test, becoming the third Pakistani batsmen to reach the milestone behind Javed Miandad (8832) and Inzamam-ul Haq (8829).
In all 28 batsmen in the world have scored 8,000 or more Test runs.
Misbah also completed his hundred with a reverse sweep off Maxwell, taking 166 balls for the mark before he gave a return catch to Steve Smith.
Misbah hit ten boundaries and a six and added 181 runs with Younis to further hit Australia badly.
With a big first innings total in sight Pakistan can now hope of clinching their first series win over Australia since 1994. They won the first Test by 221 runs in Dubai.
The Younis-Misbah stand flourished in the afternoon as Australian bowlers toiled hard in the morning session to get only one wicket of Azhar Ali (109).
Pakistan added 101 in an extended two-and-a-half hours session due to Friday prayers after resuming at 304-2.
Younis added 236 with Ali which erased the previous highest third wicket stand against Australia of 223 held by Javed Miandad and Taslim Arif from a 1980 match in Faisalabad, Pakistan.
Australia had another unusually 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.
Haddin had to walk off the field and Warner, who replace him behind the stumps, spurned a stumping chance off spinner Nathan Lyon as Younis was well out of his crease on 125.
But Warner made amends as he took a good catch off Ali’s glance off paceman Mitchell Starc for a consolation wicket. – AFP