Chasing a target of 150, Pakistan's spin trio of Raza Hassan, Mohammed Hafeez and Saeed Ajmal restricted the Aussies to 117 for seven.
With this win, Pakistan now have four points and, with a healthy net run-rate of + 0. 273, will hope South Africa, who are already out of the tournament, beat India or lose by less than 32 runs.
Australia needed to reach the target of 112 in order to ensure a semi-final berth and Mike Hussey, with an innings of 54 off 47 balls, ensured his team had enough runs to move into the round of four.
Ajmal, with three for 17, was well complemented by Hafeez and Raza who chipped in with a couple of wickets each.
Hussey's square cut off the first delivery of the 20th over bowled by Umar Gul took Australia past the magic figure of 112 and there was a big round of applause from the dug-out.
It was rookie left-arm spinner Raza who got the prized scalp of Shane Watson for eight. The ball dipped into the opener as he went for a sweep shot but missed it completely to be adjudged leg-before.
David Warner followed suit as he also tried to sweep his way out of trouble only to be trapped plumb in-front off Hafeez's bowling.
Skipper George Bailey (15) and Cameron White (12) did hit a six each but lack of match-time showed in their batting as they were unable to read the Pakistani spinners properly.
Earlier, an impressive half century by Nasir Jamshed and useful contributions from Kamran Akmal and Abdul Razzaq helped Pakistan post a competitive 149 for six after being put into bat.
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