Skipper Steve Smith did not enforce the follow-on after Pakistan were dismissed for 142, some 287 runs behind on the first innings.
Instead Australia amassed a formidable lead over the beleaguered tourists heading into the tricky twilight session under lights.
Smith went after the runs and brought up his 19th Test half-century off 59 balls with his eye on a declaration.
But he was caught at long-on by Rahat Ali going for a heave off leg-spinner Yasir Shah for 63 off 70 balls with 11 fours.
Nic Maddinson once again failed and was out for four off just three balls before he was caught off Wahab Riaz.
Both openers were out before tea. David Warner fell for 12 when he went to hit Mohammad Amir through midwicket only to miscue his pull shot to Wahab Riaz at mid-on, while Matthew Renshaw was caught at second slip off Rahat Ali for six.
The highest winning run chase in the fourth innings at the Gabba stands at 236 for seven by Australia against the West Indies in 1951.
Earlier Pakistan's last two partnerships battled for almost an hour before they were all out for 142 to trail Australia by 287 runs.
Wicketkeeper Sarfraz Ahmed earlier top scored with a fighting unbeaten 59 off 64 balls as the tourists added 45 runs to their overnight total 97 for eight.
Sarfraz and Mohammad Amir put on a stubborn 54 runs for the ninth wicket before Amir was adjudicated caught behind off a faint edge, detected by Hot Spot.
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