Imad Wasim, playing in his first worldwide match in almost a year caused havoc with his slow left-armers dismissing both openers in the first over and unveiling his new Cristiano Ronaldo-inspired celebration in the process.
Paceman Faheem Ashraf and Shaheen Afridi both took two wickets apiece for Pakistan.
Ashton Agar and Nathan Coulter-Nile eased the pain of an embarrassing thrashing, partnering for 38 runs in seven overs before Pakistan cleaned up the tail-end.
Babar held the Pakistan innings together as the hosts reached 155-8, before left arm spinner Imad claimed 3-20 in four overs in his first game in over a year as Australia were bowled out for 89.
Only twice have Australia scored fewer runs in a T20 worldwide, making just 79 against England at Southampton in 2005 and 86 in a defeat by India at Dhaka four years ago. However, a disastrous middle-overs collapse from Pakistan, in which they lost six wickets for 23 runs, gave Australia momentum.
Sophie Molinuex's brilliant 4-16 helped Australia take a 1-0 T20 series lead.
Having been dismissed for a golden duck, Imad wasted no time in making an impact with the ball, Aaron Finch chopping on without scoring and Short also dragging on in a dramatic first over.
"That Powerplay was horrific.it was like a vehicle crash in slow motion", Finch said.
"There was no luck there it was pretty embarrassing to be honest", Finch said.
"Obviously we were just outplayed".
Things went from bad to worse for the tourists, Alex Carey edging Imad behind and Chris Lynn losing his off stump after being deceived by a Faheem delivery, leaving Australia 22-6 in the sixth over.
Billy Stanlake (3/21) and Andrew Tye (3/24) were in great form and it seemed like Pakistan had thrown away the advantage.
White-ball superstar Babar Azam finished unbeaten on 68 while Mohammad Hafeez crunched two sixes on the way to 39. Part-time spinner D'Arcy Short had Hafeez top-edging to long-on and Asif Ali was caught plumb leg before wicket by legspinner Adam Zampa.
For Pakistan, they'll have fewer selection considerations to make ahead of the second T20I at Dubai on Friday if any at all.