Batting at number four, and seeing wickets tumbling around her, Mooney hit 109 off 114 balls and found a steady partner in Alana King (51 not out off 49 balls) as Australia posted a total of 221-9 in their 50 overs.
The Aussie bowlers then got to work and never let Pakistan back into the encounter, the Asian side eventually folding to be 114 all out.
After being sent in to bat at the toss, Australia skipper Alyssa Healy batted herself into a decent position but was left frustrated after sending a simple catch to Diana Baig to see her depart for 20 from 23.
Phoebe Litchfield fell three balls later and the wobble was firmly on as Ellyse Perry, Annabel Sutherland and Ashleigh Gardner all departed for low single figures.
Nashra Sandhu (3-37) and Rameen Shamim (2-29) shared the wickets of that trio and picked up the next two between them as Pakistan turned the screw with eyes on a first-ever win over Australia.
Tahlia McGrath fell for five before Georgia Wareham departed for a duck as the spin twins were both economical and effective.
At 76-7, Australia desperately needed someone to stick with Mooney, who masterfully rotated the strike and avoided the aerial shots that had caused her teammates so many problems.
Kim Garth proved to be an able running partner, with the fast bowler making 11 off 47 balls before she was stumped by Sidra Nawaz down the leg side in a wonderful display of wicketkeeping.
There was only a little panic from Australia, finding themselves at 115-8, as King came in to support Mooney with big hitting so often a feature of her innings.
However, the spinner kept things calm as Mooney neared her century, which she duly reached with a single, her first World Cup 100 coming from 110 balls.
From there, the pairing went big, as their partnership passed 100 and only ended on the final ball as Mooney was caught for 109 from 114 balls.
King provided 51 from 49 balls including three sixes to become the first batter in women’s ODIs to score a fifty while batting at number 10 or lower.
It meant that after suffering an almighty scare, Australia had recovered to set Pakistan 222 to win.
While spin had done for the majority of Australia's wickets, they relied on pace with Megan Schutt having been brought in to replace Sophie Molineux.
A steady start to Pakistan's chase was required but Sadaf Shamas departed for five as she was caught behind by Alyssa Healy off the bowling of Kim Garth on review.
Annabel Sutherland took a low catch for Schutt’s first wicket before the experiment to send Sidra Nawaz higher up the order did not work out as she was dismissed for five by Garth.
With Natalia Pervaiz and Eyman Fatima falling cheaply, Pakistan slipped to 31 for five inside the ninth over.
Sutherland became the third pace bowler to pick up a wicket as skipper Fatima had to return to the hutch.
Sidra Amin dug in but became the first wicket to spin in the innings as Gardner dismissed her for 35, while Georgia Wareham picked up the next wicket to leave Pakistan 86-8.
King was the third of the spin trio to earn a wicket as she broke a building partnership before Sutherland bowled Rameen to secure Australia their second win of the World Cup.
Nadine de Klerk once again proved to be the hero with the bat as the Proteas Women held their nerve to beat Bangladesh by three wickets with three balls to spare at the ICC Women's World Cup.
Tony de Zorzi was standing firm on 81 not out but the Proteas suffered a batting collapse to hand Pakistan the advantage at stumps on the second day of the first Test in Lahore.
Australia captain Pat Cummins admits he is "less likely than likely" to be fit for the first Ashes against England that starts in Perth on 21 November.
Australia captain Alyssa Healy struck a superb century to guide her team to a three-wicket win against India at the ICC Women's World Cup in what was a record run-chase.
