After setting an imposing 438-run target, Pakistan rattled the Australians through a brace of wickets apiece from spinners Zulfiqar Babar and Yasir Shah to leave Australia tottering on 59-4 at stumps on the fourth day, needing six wickets for a 1-0 lead in the two-Test series.
Chris Rogers (23) and Steven Smith (three) were at the crease as Australia need another 379 for an unlikely win.
Australia had raced to 44-0 before Babar struck twice in the 14th over, inducing David Warner, who had scored his third successive test century in the first innings, to come out of the crease for a smart stumping when he was on 29 with his first ball and then trapped Alex Doolan (nought) leg before with his last.
Michael Clarke survived a review leg-before decision on nought off Shah before trapped in front of the wicket in the leg-spinner's next over for three.
Younis hit a record making 103 not out and Shehzad 131 to bolster Pakistan to 286-2 declared.
Younis added 168 for the second wicket with Shehzad as Pakistan plundered 248 runs after resuming at 38-0.
Younis swept Steve O'Keefe to square-leg boundary for his sixth boundary to get to his second hundred in the match following his 106 in Pakistan's 454 in the first innings.
Australia conceded a big 151-run lead after being dismissed for 303 in their first knock.
Younis became the seventh Pakistani batsmen, but first against Australia, to score twin hundreds in a Test.
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