Pakistan have declared on 2-286 in their second innings, setting Australia a target of 438 to win the first Test in Dubai.
Twenty-three overs remain on Saturday's fourth day of play, plus three full sessions on Sunday.
Ahmed Shehzad hit 131 and Younis Khan followed his first-innings century with an unbeaten 103 as Pakistan's batsmen dominated Australia's powerless, non-penetrative attack.
Only four times in Test history has a side successfully chased down a target of more than 400 runs and Australia can only hope their batsmen show improvement on their first-innings tally of 303.
Australia would need to set a world record to win the match.
Wicketkeeper Brad Haddin had accepted a sharp chance to remove Azhar Ali for 30 off the bowling of debutant spinner Steve O'Keefe at 1-71.
That was Australia's only joy in the first session as Pakistan went to lunch at 1-116 and the host team reached 2-231 at tea after adding 115 in the middle session.
First-year player Shehzad completed his second Test century after lunch off 208 deliveries, gazing skywards in celebration.
The 22-year-old Shehzad smashed 10 fours and four sixes in his five-hour knock.
As Pakistan chased quick runs after tea, Shehzad went for a reverse sweep and was out lbw to O'Keefe at 2-239 after adding 168 for the second wicket with Younis.
Younis hit six fours and two sixes off 152 balls.
O'Keefe claimed 2-112 off 27 overs while fellow spinner Nathan Lyon finished with 0-72 off 18.
HIGHEST SUCCESSFUL FOURTH-INNINGS RUN CHASES IN TESTS:
* West Indies 7-418 v Australia, May 2003, St John's in Antigua
* South Africa 4-414 v Australia, Dec 2008, WACA Ground in Perth
* India 4-406 v West Indies, April 1976, Port of Spain in Trinidad
* Australia 3-404 v England, July 1948, Headingley in Leeds
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