Debutant Pakistan off-spinner Bilal Asif ripped through the Australian middle-order with six wickets as the visitors were bowled out for 202 on the third day of the first Test, in Dubai, on Tuesday.
Australia openers Usman Khawaja and Aaron Finch had launched a strong reply to Pakistan's first innings total of 482, reaching 137-0 without at lunch.
Pakistan were rewarded for their intelligent field placement as the tourist lost their first wicket at 142, with Finch caught for 62 after a sharp catch at silly mid-on from Asad Shafiq.
But the second session belonged to the 33-year-old Asif, who made full use of a lively pitch at the Dubai International Cricket Stadium and dismissed Khawaja (85), Shaun Marsh (7), Travis Head (0) and Marnus Labuschagne (0) in the space of 11 runs.
Asif finished with an impressive 6-36, while seamer Mohammad Abbas grabbed 4-29.
Pakistan earned a commanding first innings lead of 280 runs but captain Sarfaraz Ahmed decided not to enforce the follow-on.
They returned to bat for the final hour with Imam-ul-Haq and Mohammad Hafeez adding just 37 for the opening wicket, in contrast to 205 runs they scored in the first innings.
Left-arm spinner Jon Holland removed Hafeez for 17 in the 13th over before nightwatchman Asif was sent back for a duck by off-spinner Nathan Lyon.
Azhar Ali was trapped leg before for four runs by Holland as Pakistan finished the day at 45-3, extending their overall lead to 325 runs with two days to play.
Abu Dhabi will host the second and final Test from October 16.