The 35-year-old became the first player to score three consecutive centuries against Australia since legendary Englishman Herbert Sutcliffe achieved that feat way back in 1925.
Younis made tons in both innings as Pakistan won the first Test by 221 runs in Dubai last week, and the in-form batsman put them on course to win the two-match series by making a sublime 111 not out in an unbroken stand of 208 with Azhar Ali (101no), who scored his first century against Australia.
Pakistan, who can move above England into third in the International Cricket Council (ICC) rankings by claiming a series whitewash, were in command on 304-2 at stumps as Australia's bowlers toiled in the heat.
Younis' future at international level appeared to be in doubt when he reacted angrily to being omitted from the one-day international squad to face Australia - and he has proved a point to the selectors in emphatic fashion in the ensuing Tests.
The elegant right-hander last week became the first Pakistan player to score a century against all nine Test-playing nations and is also his country's leading century-maker in Test cricket, with his latest knock taking his tally to 27.
Azhar gave great support to the man of the moment with a sublime knock to ensure Australia's hopes of squaring the series look remote, as Pakistan appear on course for a first Test series win against them for 20 years.
The tourists responded to their first Test defeat by dropping Alex Doolan and Steve O'Keefe and bringing in Glenn Maxwell and Mitchell Starc.
After winning the toss and electing to bat first, Pakistan made a solid start before Ahmed Shehzad (35] was trapped leg before by Nathan Lyon (1-86) with 57 runs on the board.
Pakistan were two down for the loss of 96 when Mohammad Hafeez (45) edged Mitchell Johnson (1-50) through to Brad Haddin, but that was as good as it got for the tourists.
Mitchell Marsh got one to nip back in at Younis, who was on 23 at the time, and struck him in front, but it was not clear if the ball had hit bat or pad first and Australia captain Michael Clarke opted against a review in any case.
Clarke must have been wishing he had taken a chance when Younis and Azhar set about compiling a huge third-wicket partnership to leave the tourists up against it.
The in-form Younis brought up three figures yet again by dispatching Lyon over his head for four and Azhar's century came from what proved to be the penultimate delivery of the day, punching Marsh through the covers for three.
Azhar struck four boundaries in his patient 223-ball knock, with Younis taking the role of aggressor with 10 fours and a six from 155 deliveries on another memorable day for Pakistan.