The Kangaroos began the third day at 30/0 with Khawaja and Finch batting at 17 and 13 runs, respectively.
Pakistan 3-255 at stumps on day one at Dubai International Cricket Stadium. Hafeez registered a century as he and his opening partner Imam-ul Haq (76) shared a 201-run partnership for the first wicket.
The second hour, however, saw runs scored at a much faster pace.
Hafeez, whose last of 50 Test appearances came in England two years ago, brought up his hundred by pushing spinner Jon Holland for two after hitting a pair of boundaries off Mitchell Starc the previous over. There were the odd LBW shouts and the occasional play and miss, but both Sohail and Shafiq looked largely settled on a track which had very little to offer to the bowlers.
Finch, Head, Marnus Labuschagne and Michael Neser are all likely to make Test debuts in Dubai.
"That was probably the biggest mistake we made today".
Australia lost that match by 492 runs.
Akshay Kumar cancels Housefull 4’s shooting, Sajid Khan steps down as director
He'll do things to me and give me orgasm and teach me the art of sex but maybe he won't actually put his dick inside me. She also said that 'I'm sure he's done this to so many other girls, I just want them to know they're not alone'.
Babar Azam was the other unbeaten batsman on three. Sohail punched Holland to short midwicket and set off for a run.
At 418 for 6, Pakistan still had a good total on the board but needed a few more to feel absolutely safe.
Yasir had shaken the Australian innings with 4-114 but Australia clung on.
Finch dropped Ahmed in the first slip but made amends through a direct throw at the non-striker's end to run out the Pakistan captain.
In Shadab's absence - he is out with a groin injury - Pakistan can call on the uncapped 33-year-old offspinner Bilal Asif who last played an ODI in 2015. Wahab Riaz flicked Siddle for a four while Yasir Shah collected three in the same over.
Neser, 28, could edge out the recalled Peter Siddle who did not bowl in the four-day match with Pakistan A. And with Matt Renshaw's participation in doubt following his blow to the head while fielding, Labuschange could slot in alongside Finch at the top of the order.
Sarfraz admitted Pakistan's batsmen will also face challenge against Australia's veteran spinner Nathan Lyon who took 8-103 in the drawn tour game in Dubai earlier this week.
Khawaja, though, looked more steady than he historically has in Asia, and will look to kick on tomorrow on what is still a pitch you'd rather bat than bowl on.