Chasing 351 to win, Pakistan are 5-190, with captain Babar Azam not out 46, at tea on Friday's last day of play in Lahore.
Australia have a minimum 37 overs in the last session to capture the remaining wickets to win the Test and claim the three-match series 1-0.
The hosts resumed on the final day at 0-73 but lost two wickets in the opening session and another three in the middle session.
Australian spinner Nathan Lyon has taken 2-67, captain Pat Cummins has 2-23 and allrounder Cameron Green 1-18.
Green claimed the initial breakthrough, removing opener Abdullah Shafique for 27 in the fourth over of the day.
Shafique played forward defensively to a Green delivery which nicked the outside edge to present wicketkeeper Alex Carey a simple catch.
Some 15 overs later, Lyon claimed the Azhar Ali's wicket, courtesy of a successful video review.
Azhar (17) attempted a sweep shot but the ball lobbed to Steve Smith at slip who, along with other Australians, immediately appealed for a catch.
Umpire Ahsan Raza ruled not out and Australia sought a review.
Replays showed the faintest of audio spikes when the ball passed Azhar's bat before hitting his pad en route to Smith.
After lunch, Lyon dismissed Imam-ul-Haq (70) when the opener edged onto his pads and was caught by Marnus Labuschagne at silly point.
And seven overs later, captain Cummins trapped Fawad Alam lbw for 11 when the lefthander missed a fullish delivery - he sought a review but replays showed the ball would have struck between middle and off stumps.
In his next over, Cummins produced a superb inswinger which struck Mohammad Rizwan on the front foot and he was given out, lbw, for a duck.
Rizwan opted not to review the decision but replays showed the ball struck him outside the line of off stump.
His departure left Pakistan 5-167 and the home side's hopes of their highest successful run-chase on home soil, topping the 1994 team's effort in making 314 against Mark Taylor's Australian team in Karachi, had disappeared.
Their predicament could have been worse, with Babar, on 45, dropped by Travis Head at deep square leg from Lyon's bowling in the last over before tea.
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