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.
The left-hander, in his 110th Test, responded in typical swashbuckling fashion, crashing 15 fours and one giant six in his 149-ball knock.
The opening batsman had wanted to wear the shoes during the match at Perth with the hand-written messages "Freedom is a human right" and "All lives are equal" clearly visible.
Australian cricketer Usman Khawaja vowed Wednesday to fight a ban on him wearing shoes during a match highlighting the plight of people in Gaza, saying it was a "humanitarian appeal" and not a political message.
Batter Khawaja had the messages "Freedom is a human right" and "All lives are equal" written on his boots in the colours of the Palestinian flag in Tuesday's training for the first test against Pakistan.
"Any sort of moment you can get to have a few days or a week just to get away from the game and get your mental side back to a position where you can go out and perform internationally, it's important," he said.