However, Mitchell Marsh (57 not out) and Steve Smith (26 not out) are leading an Australian fightback, powering the hosts to 4-107 at tea on day three at the MCG.
Australia's position, a lead of 161 in their second innings, could have been much worse after Pakistan quicks Shaheen Afridi (2-40) and Mir Hamza (2-13) caused havoc either side of the lunch break.
Hamza was on a hat-trick after bowling David Warner (6) and Travis Head (first-ball duck) in consecutive balls to restrict Australia to 4-16.
The devastating spell brought back memories of Pakistan's heyday when the likes of Waqar Younis, Wasim Akram and Imran Khan terrorised batters with wild swing bowling.
Warner was given a standing ovation from the MCG crowd after departing the arena in what was his final Test innings at the famous ground ahead of his retirement following next week's series finale in Sydney.
Pakistan would have been in full control of the Test had opening batter Abdullah Shafique not put down a simple catch in slips for the second time in three days.
After dropping Warner in the third over the match in the first innings, Shafique spilled a golden opportunity off Marsh when Australia were 4-46.
"It's like a crocodile jaw trying to catch a ball."— cricket.com.au (@cricketcomau) Abdullah Shafique hands Mitch Marsh a life on 20 #AUSvPAK pic.twitter.com/NMlTKHn3t5December 28, 2023
"This was a big, big opportunity … this might be the difference between winning and losing this game," Pakistan legend Waqar Younis said in commentary on the Seven Network.
"Pakistan fought so, so hard through all of this match and that catch might cost them this match."
Australia went to lunch at 2-6 after Usman Khawaja and Marnus Labuschagne both fell in a chaotic 15-minute period.
Labuschagne (4) was out to Afridi on the final ball of the first session after opener Khawaja survived just two balls to the Pakistani left-armer.
Australia were forced to bat for a tricky period before the break on Thursday after Pakistan were bowled out for 264.
Skipper Pat Cummins (centre) took five wickets to dismiss Pakistan for 264 in their first innings. (Joel Carrett/AAP PHOTOS)
Earlier, captain Pat Cummins took his 10th five-wicket haul in Tests to help end Pakistan's innings.
Cummins, who swung the second Test in Australia's favour late on day two, grabbed two wickets on Thursday morning to finish with figures of 5-48.
Pakistan's notoriously brittle tail showed far more resistance than expected to push their overnight score from 6-194 in reply to Australia's 318.
Fast bowler Aamir Jamal frustrated Australia's star bowling attack, smashing an unbeaten 33 in just his second Test.
Afridi (21), who averages 6.74 with the bat, also thrashed his way to his highest Test score.
Shaheen Afridi threw his bat with some success during Pakistan's first innings at the MCG. (Joel Carrett/AAP PHOTOS)
Cummins had tremendous support from spinner Nathan Lyon (4-73), who has the fifth-most Test scalps at the MCG to show no sign of slowing down after entering the 500-wicket club during the first Test in Perth.
The fast-bowling skipper has raced to 247 career scalps from 57 Tests.
For Australian bowlers who have taken more than 100 Test wickets, Cummins has the best strike-rate (47.25), with Mitchell Starc (48.94) next.
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