Chasing 192 to clinch the Group Two super 10 match, Australia were cruising at 126 for two in the 12th over before the Pakistan bowlers turned the match on its head.
Zulfiqar Babar, Umar Gul, Shahid Afridi and Bilawal Bhatti claimed two wickets each as Australia were all out for 175.
Australia's Glenn Maxwell blasted six sixes in a sizzling 74 and featured in a century-plus stand with Aaron Finch (65) but their efforts proved in vain.
Australia lost quick wickets as David Warner and Shane Watson went in the first over before Maxwell came to the crease and set the stadium alight with some breathtaking power-hitting.
Finch played second fiddle and the duo's dominance was in full display in the 12th over of the innings, sent down by a hapless Bhatti, which yielded 30 runs.
But when Maxwell departed after 33 balls of swashbuckling entertainment it triggered a collapse Australia could not recover from.
"Two outstanding innings from Max and Finchy, that's really good for us but from there you'd love to finish it off," Australia captain George Bailey told reporters.
"(It was) an outstanding fightback from Max and Finchy to get ourselves back into the game after losing our two most destructive batters in the first over.
"For them to rebuild and get the momentum back and maybe to get the game to the stage where we should have won was outstanding."
Umar Akmal fell six runs short of his maiden Twenty20 International century as his 54-run blitz powered Pakistan to 191 for five.
Pakistan, who looked determined to shrug off Friday's defeat to arch-rivals India, were 25-2 in the fifth over when Umar walked in to join brother Kamran Akmal (31) and they shared a 96-run partnership in 8.3 overs.
The 23-year-old Umar received a let-off as Brad Hogg, who at the age of 43 became the oldest cricketer to play a Twenty20 International, dropped him in the deep when he was on 22.
But the right-hander looked unstoppable as he hit four sixes and nine fours before falling in the first ball off the final over.
"It was the best knock of my career simply because we were under tremendous stress having lost our first match (to India)," said Umar, who passed fitness test earlier in the afternoon after struggling with a hamstring problem.
"It was very important to win this match. Team management backed me to go out and express myself with the bat and I played my natural game.
"It was good to have a partnership with brother, we were playing together after a while."
- Sports & Recreation
- Glenn Maxwell
- Umar Gul
- Shahid Afridi
- Bilawal Bhatti
- David Warner