Pakistan vs Australia: Live cricket score
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.
Jamshed made 55 off 46 balls and along with Akmal added 79 runs for the third wicket. Akmal made 32 off 26 balls with the help of a four and a six.
Abdul Razzaq's 22 off 17 balls helped Pakistan in closing in on the 150-run mark while left-arm seamer Mitchell Starc was the pick of the Australian bowlers with brilliant figures of three for 20 in his four-over spell.
Hafeez was the first one to walk back to the dug-out when Starc's inswinging delivery caught him plumb in-front after he had made only four.
The normally fluent Imran Nazir struck a couple of boundaries but was out in the most disappointing manner when he closed the face of his bat to a tame full toss from Shane Watson and was caught in the mid-off region.
At 29 for two, Kamran and Jamshed got together and resurrected the innings. Initially, the duo depended a lot on singles and twos but after getting set, hit some great shots.
Jamshed pulled a bouncer from Pat Cummins in a superb fashion behind square for his first six, the ball landing in the stands.
He then slogged left-arm spinner Xavier Doherty over deep mid-wicket for his second six. A lofted drive over Watson's head for a one bounce four was also pleasing to the eye.
Kamran, who hasn't had a good time with the willow, finally got some runs under his belt. A six off Hogg over long on showed that the controversial glovesman was ready to prove his critics wrong.
Jamshed got to his second half-century of the tournament with a lofted boundary off Hogg. He achieved the feat in 41 balls and, with the help of four fours and two sixes.
He was finally out when he tried to give Doherty the charge but could only find the long-on fielder.
Akmal soon followed as he offered a low catch to Cameron White off Starc who had come back for his second spell.
From 108 for two, Pakistan had suddenly slumped to 108 for four. Abdul Razzaq, in company of Umar Akmal, hit a few lusty blows towards the end of the innings to give the total a respectable look.