Pakistan lost opener Mohammad Hafeez early in their second innings but were still at 51-1 at tea on the second day of the second Test in Abu Dhabi on Wednesday.
Fakhar Zaman was unbeaten on 32 and Azhar Ali on 12 not out as Pakistan stretched their lead to 188 with eight wickets in hand to force a 1-0 win in the two-match series.
Hafeez, who scored a hundred in the drawn first Test in Dubai, fell to a lazy shot off pacer Mitchell Starc, caught at short mid-off for six.
Earlier, medium pacer Mohammad Abbas (5-33) and spinner Bilal Asif (3-23) wrecked Australia for 145 in their innings.
Abbas had Shaun Marsh, in the fourth over of the day, for three and Travis Head for 14 before wrapping up the innings by trapping Starc leg-before for 34.
This becomes Abbas's third five-wicket haul in a burgeoning career of ten Tests.
Asif had removed Aaron Finch (39) and in the last over before lunch trapped Tim Paine leg-before for three.
Marnus Labuschagne offered some resistance during his 25 before falling to a freakish run out, backing up too far as a drive from Starc was deflected to the stumps by Yasir Shah with Labuschagne out of his crease.
Abbas, whose first wicket of the match made him the joint second fastest Pakistani to 50 wickets, gave Pakistan an early wicket in the fourth over of the day, removing Marsh with a catch in the slip.
He then had Head caught in the second slip to leave Australia at 56-4.
Leg-spinner Yasir made it 75-5 with the wicket of Mitchell Marsh, caught close to the wicket for 13 before Australia lose two more to reach lunch at 91-7.