After the two teams shared the opening two matches, Pakistan secured the series 2-1 with a composed chase of 158, reaching the target with 49 balls to spare.
Australia struggled throughout their innings after being sent in to bat. Captain Josh Inglis fought a lone battle with 65 off 71 balls, but no other batter managed to cross 20 as Pakistan's bowlers kept the visitors under constant pressure.
Shaheen Shah Afridi led the charge with 3 for 30, while Abrar Ahmed and Shadab Khan picked up two wickets each as Australia were bundled out for 157 in 42 overs.
In reply, Pakistan were tested by Australia's spinners but never lost control of the chase. Babar Azam anchored the innings with 40, while Maaz Sadaqat contributed 27 at the top.
After a brief middle-order wobble left the hosts at 112 for 6, Shadab Khan (29*) and Abdul Samad (18*) guided Pakistan home with an unbeaten 49-run partnership.
Matthew Kuhnemann was Australia's standout bowler, claiming 3 for 38, while Nathan Ellis, Matt Renshaw and Matthew Short took a wicket each.
The series victory gives Pakistan valuable momentum ahead of the upcoming ODI World Cup, while Australia will now turn their attention to their tour of Bangladesh.
Australia are scheduled to arrive in Dhaka for a white-ball tour comprising three ODIs and three T20Is.
The ODI series begins on June 9 at the Sher-e-Bangla National Cricket Stadium, with the visitors looking to bounce back quickly from their series defeat in Pakistan.
