Cameron Murray stepped up to rescue Australia and continue their remarkable World Cup record.
The reigning champions were trailing in a thrilling Elland Road semi-final when the South Sydney star charged through some unusually feeble Kiwi defence in the 53rd minute.
Nathan Cleary converted and Mal Meninga’s side clung on for a place in next Saturday’s final against either England or Samoa.
The only time they have not made a World Cup final is when Great Britain beat France in the inaugural event in 1954.
They have won eight of the last nine tournaments since the Lions' 1972 success.
New Zealand were the only side to break that remarkable sequence, stunning the Kangaroos in 2008.
And they started in confident fashion here, spreading the ball at every opportunity.
They scored a brilliant opener, Joseph Manu collecting Dyan Brown’s crossfield kick and managing an exquisite offload to Jahrome Hughes as he fell.
Jordan Rapana slotted the first of his three goals but ‘Roos hit back with an even better effort.
Josh Addo-Carr showed why he’s rated rugby league’s fastest player, racing 30m to catch Ben Hunt’s kick on the full for his 12th World Cup try.
That equalled team-mate Valentine Holmes’ tournament record and Cleary improved.
But - after Rapana’s penalty - Holmes soon reclaimed it after a miracle pass from a sidestepping Jack Wighton.
The sublime tries kept coming. Dylan Brown finished a slick move in the 37th minute after Nelson Asofa-Solomona blasted a hole in Australia’s middle and the Kiwis sent Ronaldo Mulitalo clear down the right.
Rapana’s conversion left his side 14-10 at the break and they thought they’d extended that when Peta Hiku crossed only for it to be chalked off.
Murray was at the heart of a melee as things boiled over but he stayed cool for the killer moment, the Kiwis heartbroken when a second Hiku effort was ruled out late on.
