Pakistan lost their first wicket in the fifth over when Azhar Ali was well caught by a diving Usman Khawaja at third slip off Mitchell Starc for five.
At the interval, Pakistan were 20 for one with Sami Aslam on three and Babar Azam not out on nine.
Peter Handscomb earlier posted a maiden century and the tail wagged as Australia extended their first innings to frustrate Pakistan.
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.
Handscomb was out in the third over 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.
Bird smoked a lusty six in his unbeaten 19 and Lyon cracked 29 off 24 balls to stymie Pakistan's efforts to quickly mop up the Australia first innings.
It mitigated Pakistan's hard work in the first session when they claimed four dismissals but were left to rue yet more dropped catches.
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.
Smith was finally out to a wild shot in the 100th over when he slashed at Wahab Riaz and gave wicketkeeper Sarfraz Ahmed a regulation catch.
It ended a 172-run stand with Handscomb and he departed with his side in command at 323 for four.
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.
Maddinson was dropped by Azhar at short leg before scoring but was out soon after, caught behind off Wahab.
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