The 36-year-old right hander scored 106 for his 25th century to help Pakistan counter the fiery pace of Mitchell Johnson (3-22) after Pakistan won the toss and decided to bat on a flat, grass-less Dubai stadium pitch.
At close, skipper Misbah-ul Haq was unbeaten on 34 and with him Asad Shafiq not out nine.
Batting on 99, Younis jumped out of his crease to hit off-spinner Nathan Lyon for a big six to reach the three-figure mark off 220 balls, equalling Pakistan's record for most hundreds held by Inzamam-ul Haq.
He also became the first Pakistani to score a hundred against all nine Test opponents, and overall the 12th batsmen in the world to reach the honour.
Younis said he felt proud at helping the team and achieve a rare honour.
"When you play with your heart, things go your way and I am proud to be the first Pakistani to score hundreds against all countries and to equal the great Inzamam's record," said Younis.
"If we manage to score 400 plus we can put Australia under pressure but it's not going to be easy because they have bowled well especially Johnson."
In all Younis batted for five hours and 17 minutes and hit ten boundaries and a six.
Younis added 108 for the third wicket with Azhar Ali (53) and another valuable 83 with Misbah to steady the innings.
He played an innings of maturity and guile after Pakistan had lost both openers by the fourth over, with Mohammad Hafeez (nought) and Ahmed Shehzad (three) dismissed by Johnson and pace partner Peter Siddle.
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