Younis notched a memorable 213 for his fifth double hundred to steer Pakistan to 570-6 declared in their first innings on a flat Sheik Zayed Stadium pitch here.
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.
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.
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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.
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.