Boasting a healthy score of 304-2 after the first day's play, Pakistan pressed on to an imposing total of 570-6 declared in Abu Dhabi, with Younis - a twin centurion in last week's first Test - reaching 213.
Misbah-ul-Haq (101) followed Younis and Azhar Ali (109), who completed his hundred on day one, to three figures, piling further misery on Australia after their 221-run defeat in Dubai.
Captain Misbah finally called a halt to Pakistan's innings after 164 overs, and there was a further setback for the tourists when Chris Rogers departed for five before stumps.
Australia closed on 22-1, with David Warner (16) and nightwatchman Nathan Lyon (one) unbeaten, and now face a huge challenge to avoid a first series defeat against Pakistan since 1994.
The mammoth third-wicket partnership between Azhar and Younis finally came to an end in the 11th over of day two.
Warner - standing in as wicketkeeper after Brad Haddin hurt his shoulder early in the day - dived to his left to catch Azhar down the leg side off Mitchell Starc (2-86) and break a stand worth 236.
Younis was undeterred and pressed on alongside Misbah as Pakistan's number three, four and five batsmen made centuries in the same Test innings for the first time.
The veteran pair put on 181, with Misbah striking 11 boundaries before being caught and bowled by Steve Smith (1-41).
The third umpire was needed to confirm Misbah's dismissal, amid suspicions of a bump ball, before Younis brought up his double-century and moved past the 8,000-run mark in Tests as a result.
Younis' spell at the crease eventually came to an end in the 156th over of the innings, from the 349th delivery he faced.
Looking to add to his two sixes, he attempted to slog Peter Siddle (1-75) over the leg side but inside-edged onto his stumps, leaving the field to congratulations from Australian captain Michael Clarke and the Abu Dhabi crowd.
Asad Shafiq (21) became Starc's second victim shortly before Pakistan declared, although there was time for Australia's bad day at the office to get worse as Rogers was caught behind by Sarfraz Ahmed off Imran Khan (1-18).