Younis notched a memorable 213 for his fifth double hundred and Misbah-ul Haq notched his sixth century to guide Pakistan to 570-6 declared in their first innings on a flat Sheik Zayed Stadium pitch in Abu Dhabi.
At the close on day two Australia were 22-1 with David Warner on 16 and nightwatchman Nathan Lyon on one, still trailing by 548 runs with nine wickets intact on a day when Pakistan skipper Misbah-ul Haq (101) and Azhar Ali (109) also enjoyed the run feast.
Opener Chris Rogers fell caught behind to paceman Imran Khan for five, putting Pakistan in a strong position to press for their first series win over Australia since 1994.
It was Younis, who hit twin hundreds in the first Test, who once again dominated Australia's hapless bowling during his eight-and-half-hour stay, hitting 15 boundaries and two sixes.
Younis hit Glenn Maxwell for a towering six and, in the spinner's next over, took a single to complete 200.
He was finally bowled while playing Peter Siddle across the line and was given a standing ovation by a 12,000 holiday crowd and his team-mates.
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.
Younis said he was delighted with his performance.
"I feel very happy and proud," said Younis. "Now it's my wish that we whitewash Australia but it won't be easy because they are a tough team."
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 10 boundaries and a six and added 181 runs with Younis to further hit Australia badly.
At 63 Misbah also became the highest scorer as Pakistan captain, beating Imran Khan's 2408 runs in 48 Tests. This is Misbah's 31st match.
The Younis-Misbah stand flourished in the afternoon after the Australian bowlers toiled hard in the morning session to get only one wicket, that of Ali.
Pakistan added 101 in an extended two-and-a-half-hour session due to Friday prayers after resuming at 304-2.
Younis added 236 with Ali to erase 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 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 replaced him behind the stumps, spurned a stumping chance off spinner 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. Ali's 250-ball knock had six boundaries, while Starc was the best bowler with 2-86.
Johnson, Lyon, Siddle and Smith had a wicket apiece.
