Pakistan have taken an unbeatable 2-0 lead in the three-match series.
Pakistan survived a late Glenn Maxwell charge to beat Australia by 11 runs in the second Twenty20 on Friday.
Maxwell, dropped twice, made 52 off 37 balls and Nathan Coulter-Nile scored a fighting 27 but Pakistan restricted Australia to 136-8.
Earlier, opening batsman Babar Azam once again top scored with 45 and together with Mohammad Hafeez (40) anchored Pakistan to 147-6 after captain Sarfraz Ahmed won the toss and opted to bat.
The victory ensured top-ranked Pakistan notches its 10th successive Twenty20 series victory under Ahmed that began with a 1-0 win over England in 2016. The last match of the series will be played at the same venue on Sunday.
"It's not easy to get 10 out 10 in Twenty20, but credit goes to the boys, the way we have improved our bowling, batting and fielding," Pakistan captain Ahmed said.
"It's a big win and now we will try to give the boys sitting on the bench a chance in the last match."
Australia top order batsmen once again choked against the left-arm spin of Imad Wasim (1-8) and legspinner Shadab Khan (2-30) before Maxwell and Coulter-Nile made a late recovery.
Wasim, who grabbed three wickets in the first match which Australia lost heavily by 66 runs on Wednesday, had the wicket of dangerman Chris Lynn.
D'Arcy Short was run-out after the ball brushed the left-arm spinner Wasim's fingers and crashed onto the stumps at the non-striker's end.
Finch's (3) struggle continued against Wasim before he holed out in the deep in Shadab's first over while attempting a desperate big shot before the legspinner had Mitchell Marsh caught behind.
"We were probably just a bit tentative in the Powerplay," Finch said. "Being six down in the last game, we tried to be conservative and when Pakistan put the squeeze on you, it can get tough. They are No.1 for a reason."
Ben McDermott was run out for the second successive time in the series by Fakhar Zaman, this time the fielder hitting the stumps with a brilliant backhand flick.
Australia was stuttering at 73-6 in the 14th over before Maxwell and Coulter-Nile put on 59 runs but both were dismissed by 18-year-old left-arm fast bowler Shaheen Afridi in the last over.
Like in the first match Pakistan innings revolved around Azam and Hafeez's 70-run second wicket stand.
Australia pegged back Pakistan through its spinners Short and Adam Zampa with Short featuring in the dismissal of both batsmen.
Hafeez holed out to Short at deep square leg while Finch caught Azam on the edge of the boundary at long off, off Short's left-arm spin.
Coulter-Nile (3-18) returned to remove Shoaib Malik (14) and Hasan Ali off successive deliveries before Faheem Ashraf's unbeaten 17 off 10 balls gave Pakistan enough runs to defend.
