Australia are now leading the five-match ODI series by 2-1.
Fast pacer Junaid Khan bowled out David Warner for 35 while Mohammad Amir dismissed Usman Khawaja soon afterwards as Australia chased 264.
Handscomb got another chance after he was bowled out but called back after Junaid's delivery was declared as a no-ball. He was dropped off another Junaid delivery later.
Pakistan batsman Babar Azam became the first Pakistani to reached 1000 ODI runs in 21 innings after he made 84 runs in the third ODI. The young batsman achieved the feat leveling the record with Sir Viv Richards, Kevin Pietersen, Jonathan Trott and Quinton de Kock.
He fell for 84 runs after Pakistan past 200. The Green Shirts were five down for 222 after 42 overs.
Shoaib Malik bowled out after an aggressive knock of 39. Opener Sharjeel Khan scored a half-century before departing.
Mohammad Hafeez, the captain in place of injured Azhar Ali, fell for 4 off a Hazlewood delivery. Asad Shafiq went for 5, leaving Pakistan three down for 99.
The hosts made two changes to the lineup that played in Melbourne on Sunday, with Mitchell Starc (rested) and Mitchell Marsh (injury) omitted for ODI debutant Peter Handscomb and fast bowler Billy Stanlake.
Handscomb, 25, was presented his maiden ODI cap, No.219 for Australia , by legendary wicketkeeper-batsman Adam Gilchrist.
Pakistan named an unchanged line-up, with Mohammad Hafeez to captain again in the absence of injured skipper Azhar Ali.
Pakistan have decided to continue with the combination of second ODI: Hafeez (c), Sharjeel, Babar, Shafiq, Malik, Akmal, Rizwan (wk), Wasim, Amir, Hasan, Junaid.
The Australian playing 11 for today is: Warner, Khawaja, Smith (c), Head, Handscomb, Maxwell, Wade (wk), Faulkner, Cummins, Hazlewood, Stanlake.