Stirling Mortlock scored an intercept try for Australia and Elton Flatley kicked five penalties and a conversion as the Wallabies shrugged off their poor form in the tournament to post an unexpected but fully deserved win.
New Zealand captain Reuben Thorne scored his team's only try while Leon MacDonald landed a conversion and a penalty as the All Blacks slipped up in the semi-finals for the second time in a row.
Australia, who won the World Cup in 1991 and 1999, play the winner of Sunday's second semi-final between England and France in next Saturday's title decider.
The Wallabies made a flying start, racing to a 13-0 lead inside the first 24 minutes, and never surrendered the lead as they produced a brilliant defensive display to shut out the All Blacks.
The game was played at a frantic pace with both sides throwing the ball around and hitting each other with ferocious defence, but it was the Australians who weathered the pressure best.
New Zealand, who committed too many fundamental mistakes, did not touch the ball until the seventh minute but almost scored a try against the run of play when flanker Richie McCaw stole the ball from a Wallabies' lineout.
The All Blacks quickly recycled the ball, then spun it wide for fullback Malili 'Mils' Muliaina who dropped the ball over the line when hit by a desperate tackle from Australian winger Lote Tuqiri.
Australia immediately made New Zealand pay for their missed opportunity when Mortlock swooped on to an attempted cut-out pass from flyhalf Carlos Spencer and sprinted 80 metres to score under the posts.
Flatley added the conversion from in front to give the Wallabies a 7-0 lead in the 10th minute, then booted another two penalties to give the defending champions a 13-0 lead.
MacDonald missed two early penalty kicks for New Zealand, but they finally got on the scoreboard five minutes before the interval when Thorne capitalised on an Australian error to score.
Wallabies flyhalf Stephen Larkham lost the ball after being caught in heavy traffic and New Zealand instinctively shifted the ball to Spencer who sidestepped his way past two defenders before offloading to Thorne to crash over.
New Zealand looked to have regained their composure with the try, but it was Australia who started the second half better with Flatley adding a quick penalty to push the lead to 16-7 after Jerry Collins infringed at the ruck.
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MacDonald pulled the margin back to nine points with a penalty midway through the second half, but another goal from Flatley gave Australia a comfortable 12 point lead, which they maintained till the end.
New Zealand -- 15 Mils Muliaina; 14 Doug Howlett, 13 Leon MacDonald, 12 Aaron Mauger, 11 Joe Rokocoko; 10 Carlos Spencer, 9 Justin Marshall (20 Byron Kelleher, 47th); 8 Jerry Collins (19 Marty Holah, 73rd), 7 Richie McCaw, 6 Reuben Thorne (c), 5 Ali Williams (18 Brad Thorn, 58th), 4 Chris Jack, 3 Greg Somerville, 2 Keven Mealamu, 1 Dave Hewett (17 Kees Meeuws, 47th)
Australia -- 15 Mat Rogers; 14 Wendell Sailor, 13 Stirling Mortlock (22 Joe Roff 72nd), 12 Elton Flatley, 11 Lote Tuqiri; 10 Stephen Larkham, 9 George Gregan (c); 8 David Lyons, 7 Phil Waugh, 6 George Smith (19 Matt Cockbain, 72nd), 5 Nathan Sharpe (18 David Giffin, 39th), 4 Justin Harrison, 3 Ben Darwin (17 Al Baxter, 49th), 2 Brendan Cannon (16 Jeremy Paul, 49th), 1 Bill Young.
Referee: Chris White (England)