Veteran batsman Younus Khan remained unbeaten on 136, his first Test century Down Under, alongside Yasir Shah, who was not out on five.
The final session of the day saw the visitors lose five batsmen, which included the wickets of Misbahul Haq, Asad Shafiq, Sarfraz Ahmed, Mohammad Amir, and Wahab Riaz. The tourists trail Australia by 267 runs.
Prior to tea, Pakistan lost their leading series run-scorer Azhar Ali as Younus closed on a century on the rain-disrupted day.
Azhar Ali was run out for 71 in a poor piece of running with Younus, when he could not beat home Mitchell Starc's throw from mid-on to the striker's end.
Day Two: Azhar, Younus lead fightback in third Test
At tea, after play finally got underway in mid-afternoon following rain, the tourists were 177 for three with Younus on 84 and skipper Misbahul Haq unbeaten on 18 to trail Australia's first innings by 361 runs.
Younus drove spinner Nathan Lyon to a diving fielder at short midwicket and hesitated, leading to some indecision with Azhar before Starc swooped in to throw back to the 'keeper standing over the stumps.
In the process Azhar passed Mohsin Khan (390) as Pakistan's highest scorer in a series in Australia, but he achieved it in three Tests, compared to Mohsin's five Tests in 1983.
In five innings, Azhar has scored 395 runs in this series at 98.75. He faced 159 balls and looked set in his 227-minute stay before the mix-up that led to his run-out.
Azhar and Younus put on 146 runs for the third wicket, restoring the Pakistan innings after they were six for two.
Azhar had survived a tight leg-before wicket review on 59 off Josh Hazlewood with the ball projected to hit the leg-stump, but not enough to overturn Sundaram Ravi's initial decision.
Day One: Australia 365-3 at stumps against Pakistan in Sydney Test
Wicketkeeper Matthew Wade was forced to leave the field with an illness shortly after play got underway, with Peter Handscomb deputising for him as he sought treatment.
Cricket Australia said Wade was suffering from diarrhoea and nausea. He fell ill in the morning and returned to the team hotel to rest and was expected to recover in time for Friday's play.
Australia have already won the series after victories in the Brisbane and Melbourne Tests, while Pakistan are battling to avoid their 12th straight Test defeat in Australia.
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