Naseem Shah was the second most impressive bowler as he took three wickets for 54, while Haris Rauf took two wickets and gave 24 runs.
"It's a special moment for me and the fans," said captain Rizwan at a post-match presentation.
"I'll give all the credit to the bowlers. Australia in Australia is not easy.
"But Saim and Abdullah have given us a couple of great starts, too," he added.
"The fans love us regardless of whether we win or lose and I really appreciate that."
"It's pretty disappointing, to be honest," said skipper Josh Inglis.
"I think after probably the first three-quarters of the first game (in Melbourne) we were totally outplayed.
"Not enough runs on the board in games two and three."
Before the start of the match, the series was finely poised at 1-1 after the hosts' two-wicket win in Melbourne before Pakistan stormed back with a dominant nine-wicket victory at Adelaide.
Pat Cummins, Mitchell Starc, Josh Hazlewood, Marnus Labuschagne and Steve Smith have all been rested for this game ahead of Australia's Test series against India beginning later this month.
In their place come pace bowlers Sean Abbott, Spencer Johnson and Lance Morris, while Marcus Stoinis and Cooper Connolly bolstered the batting.
Josh Inglis captained the side in the absence of Cummins.
In contrast, Pakistan named an unchanged side with Haris Rauf, who took 5-29 in Adelaide, leading the attack.
Australia: Matt Short, Jake Fraser-McGurk, Aaron Hardie, Josh Inglis (capt), Cooper Connolly, Marcus Stoinis, Glenn Maxwell, Sean Abbott, Adam Zampa, Spencer Johnson, Lance Morris
Pakistan: Saim Ayub, Abdullah Shafique, Babar Azam, Mohammad Rizwan (capt), Kamran Ghulam, Agha Salman, Irfan Khan, Shaheen Shah Afridi, Naseem Shah, Haris Rauf, Mohammad Hasnain.
Details of Pakistani batting:
Details of Australia batting:
Performance of Pakistani Bowlers:
Umpires: Chris Brown (NZL), Shaun Haig (NZL)
TV umpire: Chris Gaffaney (NZL)
Match referee: Dave Gilbert (AUS)
PCB Chairman Mohsin Naqvi congratulates team
Congratulating team Pakistan on their victory, Pakistan Cricket Board (PCB) Chairman Syed Mohsin Naqvi said beating a formidable team Australia on their home ground was no small feat. "The team has made us proud. Each and every player as well as the management deserve appreciation for a historic win," he said, adding, "Shaheens outclassed Kangaroos in all departments of the game be it batting, bowling or fielding."
The PCB chairman said today's win had bring smiles on people's faces. "This all was made possible by a teamwork."
He went on to say that Shaheen Shah Afridi, Haris Rauf and Naseem Shah restricted Australia to a low score. "Saim Ayub and Abdullah Shafiq again batted responsibly. Babar Azam and Rizwan were no less impressive.
President Zardari, PM Shehbaz extol players
In their messages, both President Asif Ali Zardari and Prime Minister Shehbaz Sharif praised team for showing extraordinary performance against Aussies to beat them on their home ground.
PM Shehbaz, in his post on X, said today was the big day for Pakistan cricket as the national team had beaten Australia in Australia after a gap of 22 years. "It all is the result of a teamwork," he commented.
"PCB Chairman Mohsin Naqvi and the entire team management also played their part in the historic win."
The prime minister prayed to the Almighty Allah to make today's victory the start of a glorious period for Pakistan cricket.
Punjab CM Maryam felicitates team
Punjab Chief Minister (CM) Maryam Nawaz Sharif congratulated national cricket team on their thumping victory against Australia after a lapse of twenty-two years.
In her facilitation message addressed to the national cricket team Chief Minister Maryam said Shaheens created history by defeating Kangroos on their own homeland.
Sindh Governor Tessori appreciates team performance
Sindh Governor Kamran Khan Tessori extended his heartfelt congratulations to national cricket team on winning one-day international cricket series against Australia after 22 years.
In his message, Kamran Tessori said that national cricket team brought happiness for the nation after defeating Australia by eight eights on their home ground.
He also appreciated the services of selectors, coaches, captain and all members of national cricket team.
Reporter: Awais Kiani