Babar Azam hailed Pakistan's "historic" series win over Australia after scoring another century in a nine-wicket victory.

Pakistan bowled Australia all out for 210 before comfortably chasing down their target, thanks largely to the efforts of top-order batsmen Babar (105 not out) and Imam-ul-Haq (89 not out).

Babar also recorded triple figures in Pakistan's second ODI victory on Thursday, and his consecutive centuries proved decisive in the hosts beating Australia in back-to-back home ODIs for the first time since 1982.

Writing on Twitter after his crucial haul, Babar referred to his team-mates as "superstars" and thanked Pakistan's fans for their support in Lahore.

"A historic series win for Pakistan," wrote Babar, who has now plundered 16 ODI career centuries.

"[I] couldn't have asked for more from my pack of superstars, excellent performances from Imam, Shaheen Shah Afridi, and Haris Rauf.

"To all our fans, thank you so much for your massive support!"

Pakistan head coach Saqlain Mushtaq posted: "This is historical, winning the ODI series against Australia 2-1 at home.

"Some phenomenal performances [were] witnessed by the batsmen and bowlers. Keep supporting our great Pakistan!"

Before failing to remove either Babar or Imam as they struggled with the ball, Australia lost their highest run-scorer of the series, Travis Head, to the first delivery of their own innings, leaving skipper Aaron Finch to bemoan a failure to set their hosts a more difficult target.

"We didn't get enough runs," Finch told reporters. "When you go three down in the first few overs, it's always going to be hard to get a big total."