The visitors looked to have the edge after dismissing Australia for 299.
At lunch, the tourists were 75 for four with skipper Shan Masood on 32 and wicketkeeper Mohammad Rizwan 12. Pat Cummins had taken 2-16 from five overs.
Pat Cummins confirmed on Tuesday that the same team that won the first test in Perth by 360 runs and the second in Melbourne by 79 runs would take the field for the final clash at Sydney Cricket Ground on Wednesday.
"This is my last resort, but my backpack, which contained my Baggy Green, has been taken from my luggage, which was transported to Melbourne airport and flown ... to Sydney a few days ago," he said in a post on Instagram.
At stumps, he was unbeaten on a glacial 44 off 120 balls and Travis Head was not out on nine after nearly three hours' play were lost to rain.
Last week, Khawaja spoke about how the Israel-Hamas conflict had affected him. "When I'm looking at my Instagram and seeing innocent kids, videos of them dying, passing away, that's what hit me the hardest," he said.
The Pakistan-born Khawaja, who has been keen to show his support for the people of Gaza during the ongoing conflict in the enclave, was reprimanded for wearing a black armband in the first test against Pakistan in Perth earlier this month.
Australia's Mitchell Starc said that his team was surprised at Pakistan's lack of pace, though he added that pace wasn't the "be-all and end-all" to fast bowling.
Khawaja has been denied permission by the International Cricket Council (ICC) to have a sticker showing a black dove holding an olive branch on his bat and shoes during the second Test against Pakistan.
Australia's all-formats hero’s IPL windfall, however, has not shifted his continued prioritisation of the longest format as the left-armer reiterated his desire to play every Test this summer.
Ahmed missed their 360-run defeat in Perth with leg discomfort, and while improving, he has not recovered sufficiently to take part in the Boxing Day Test at Melbourne
The Pakistan-born opener was reprimanded by cricket's global governing body on Thursday for wearing the armband during the 360-run win over Pakistan in the series-opener in Perth.
The visitors were fined 10% of their match fee and two ICC World Test Championship points were deducted from their total.
Labuschagne needed medical attention after being struck on the right hand by debutant Khurram Shahzad early in the second innings in Perth before top-edging the Pakistan quick to be out for two.
"No doubt he was missed over there in England (during this year’s Ashes series) for sure. As a captain, it makes it a lot easier knowing that bloke who has played 100-odd Test matches that knows his craft and can bowl pretty much in any conditions, you just let him get to work so it's great having him back. Yeah, another 500 to go."
Pakistan's unlikely bid to win their first Test in Australia since 1995 was left in tatters by the spin king and the home side's formidable pace attack, who wrapped up the game inside four days.
The hosts reached stumps on day three in Perth at 84-2, building their lead to 300 after bowling out the visitors on the cusp of tea for 271 in reply to their first innings 487.
Lyon was the best of the bowlers with 3-66, but he will have to wait to reach the milestone
The 37-year-old, who intends to retire from tests after the third and final game in Sydney, combined with Usman Khawaja (41) in a 126-run opening stand to get the hosts off to a strong start after winning the toss.