Australia's three-man pace attack -- Mitchell Starc, Josh Hazlewood and Jackson Bird -- decimated the tourists' first innings under the Gabba lights.
Starc and Hazlewood took three wickets each and Bird chimed in with two for seven to leave skipper Steve Smith pondering whether to enforce the follow-on after a seven-wicket final session.
At the close, Pakistan were hanging on at 97 for eight and trailing by 332 runs with Sarfraz Ahmed on 31 and Mohammad Amir not out eight.
Hazlewood put the tourists on the skids with two wickets in two balls in his fifth over.
Babar Azam got a thick edge which flew to Steve Smith at second slip for 19 and next ball veteran Younis Khan feathered to wicketkeeper Matthew Wade for a duck.
Skipper Misbah-ul-Haq was never comfortable under the lights and played well away from his body, nicking to Matthew Renshaw at first slip off Bird for four.
Sami Aslam, who was twice clocked on the helmet as he turned his head away from rising Hazlewood deliveries, was caught behind off Bird for 22 off 100 balls.
Wahab Riaz and Yasir Shah followed within minutes of each other but Sarfraz and Amir saw out play to stumps.
Handscomb made the most of his opportunity and followed up a half-century on debut against South Africa in Adelaide last month with a polished 105 in Australia's first innings of 429.
Handscomb was out shortly after tea when he chopped a Wahab delivery on to his stumps, one ball after Josh Hazlewood was caught at first slip in Mohammad Amir's previous over.
The Australians, who resumed at 288 for three, lost skipper Steve Smith for 130, Nic Maddinson for one, Matthew Wade for seven and Mitchell Starc for 10 in the first session.
Smith was finally out to a wild shot in the 100th over when he slashed at Wahab and was taken by wicketkeeper Sarfraz Ahmed, ending a 172-run stand with Handscomb.
Smith had some luck along the way with his 16th Test century, offering three chances during his 222-ball knock.
According to the infra-red imaging system Hot Spot, the pink ball registered a faint contact on the bat and Smith later admitted he had nicked it.
On 129, he jumped down the wicket to luckless leg-spinner Yasir Shah and skied to long-off, where Amir made a hash of the catch.
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