Ajmal (2-13), Hasan (2-15) and skipper Hafeez (2-24) shook the Australian batting before left-arm paceman Sohail Tanvir (3-13) wrapped up the innings in 19.3 overs. Pakistan then romped home in 14.5 overs to take a 1-0 lead in the three-match series.[break]
It was an easy win for Pakistan at Dubai Stadium after going down 2-1 in the preceding one-day series.
Shoaib Malik hit the winning boundary, finishing with nine not out while Kamran Akmal finished with an unbeaten 31 with three boundaries and a six.
The victory was never in doubt once Pakistan bowled well. Hafeez (17) and Imran Nazir (22) gave Pakistan a solid start of 30 before losing Hafeez and Nasir Jamshed (10) in quick succession.
Akmal and Malik saw off the target without any discomfort.
The second match will be played here on Friday.
Earlier Australia were let down by poor shot selection against quality spin bowling after they were sent into bat.
Australia hit only three boundaries in the innings with their last coming in the fourth over as Pakistani spinners never allowed them to settle on a turning track, reducing their opponents to their second-lowest Tweny20 total.
Opener David Warner top-scored with 22 off 25 deliveries, hitting two boundaries.
Cameron White (15) and captain George Bailey (14) were the only others to reach double figures.
Paceman Umar Gul dismissed Shane Watson (eight) in the third over while Tanvir accounted for Michael Hussey (one) in the next before Warner and Bailey put on the best stand of the innings, adding 33 for the third wicket.
Pakistan´s spinners then came into their own, as the last eight wickets went for a mere 43 runs.
Australia´s lowest Twenty20 total of 79 came against England at Southampton in 2005.
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