Pakistan resumed on 38 without loss and holding a 189-run advantage over their opponents, whom they had dismissed for 303 on Friday.
Ahmed Shehzad (131), flanked by stand-in opener Azhar Ali (30), proved difficult to budge as he reached three figures, before Younis (103 not out) became the first man since Glenn Turner in 1974 to hit two hundreds in one match against Australia.
The 36-year-old found the boundary on eight occasions on his way to becoming his country's most prolific Test century-maker - he now has 26 - and captain Misbah-ul-Haq elected to declare at 286-2 after Younis had surpassed that marker.
Younis' haul left Australia chasing a target of 438, but the tourists lost four wickets before stumps on day four to leave themselves an uphill struggle to salvage a result.
Australia's bowlers struggled to pose too many problems for Shehzad and Azhar - promoted to open after Mohammad Hafeez sustained an ankle injury in the field - and Brad Haddin's catch from a Steve O'Keefe (2-112) delivery in the 25th over provided a rare glimmer of hope for the tourists.
However, Shehzad - now joined by Younis at the crease - stepped up the pace after lunch, with the pair steadily building their respective centuries under little threat from the bowlers.
Shehzad added a further 12 boundaries to the two fours he picked up on Friday before an lbw - again from an O'Keefe delivery - ended his innings after an attempted reverse sweep.
Sarfraz Ahmed chipped in with 15 runs, before Misbah called the batsmen back to the pavilion after Younis had hit 103.
Australia's daunting chase has not started well, however.
After Chris Rogers (23 not out) and David Warner (29) had put together an opening partnership of 44 after 13.1 overs, Australia found themselves four wickets down by the end of the 17th.
Alex Doolan (0), Nathan Lyon (0) and captain Michael Clarke (3) were all dismissed lbw, while Steven Smith (3 not out) will return to the crease on Sunday with Australia requiring 379 runs.