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Australia, chasing 163 to win, were dismissed for 151 with 18-year-old left-armer Aamer taking three wickets for 27 runs in his maximum four overs - the same figures as he returned during Pakistan's 23-run win here on Monday.
The man-of-the-match struck early to remove openers David Warner and Michael Clarke before having Mitchell Johnson lbw late on to the delight of a pro-Pakistan crowd.
With just one wicket standing, a target of 19 off the last over proved beyond Australia and Shaun Tait was run out with two balls left.
Pakistan captain Shahid Afridi and fellow spinner Saeed Ajmal kept the pressure on with three middle-order wickets.
As was the case in their dramatic Twenty20 semi-final win over Pakistan in St Lucia in May, Australia's hopes, with 35 needed off the last three overs, rested with Michael Hussey.
But the left-hander, whose dashing 60 not out turned that match on its head, was lbw to paceman Umar Gul for 25, featuring four fours, when he missed an ambitious reverse sweep.
Australia's bowlers had done a good job in holding Pakistan to 162 for nine with left-arm quick Dirk Nannes striking twice in two balls to remove dangermen Umar Akmal and Shahid Afridi.
Nannes finished with three for 30 while left-arm spinner Stephen O'Keefe, on his international debut, took three for 29 including two tailend wickets.
No Pakistan batsman made more than Kamran Akmal's 33 although Aamer hit two sixes late on as he finished on 21 not out.
But no Australia batsman made more than David Hussey's 33.
Australia saw captain Clarke promote himself to opener in place of Shane Watson who, along with leg-spinner Steven Smith, was rested.
Clarke, who averaged just over 15 in Australia's run to the World Twenty20 final where they lost to England, was in superb touch while making 30 as his side slumped to 33 for three.
Warner was lbw for one to Aamer, although replays suggested the ball was narrowly missing leg-stump.
Shoaib Akhtar then had Tim Paine skying to Umar Gul at mid-off for nought.
In between those dismissals, Clarke played some superb strokes including a cover-driven four off Aamer.
But having struck six boundaries in only 17-balls he played on to Aamer.
James Hopes and David Hussey staunched the flow of wickets and Australia were 78 for three at halfway, needing 85 off the last 10 overs.
However, a fifty stand was ended when Hopes, on 30, was smartly stumped by wicketkeeper Kamran Akmal off leg-spinner Afridi.
Australia were now 83 for four in the 12th over and in need of boundaries.
Earlier, Pakistan lost Shahzaib Hasan for his second duck in as many days, although as Australia's ploy in opening the bowling with part-time spinner David Hussey was rewarded off the fourth ball when the opener was lbw sweeping.
Umar Akmal, the hero of Pakistan's win on Monday with a career-best 64, struck Johnson for a superb 'inside-out' four high over extra-cover.
But that was topped by Afridi's straight six off a near yorker-length ball from express quick Shaun Tait.
However, Nannes reduced Pakistan to 130 for six in the 17th over.
First he caught and bowled Umar, for 25, off a skied drive, that allowed the batsman to cross, and next ball he tucked up Afridi, on 18, for room and had him caught behind by wicketkeeper Paine.
