After Ella Toone gave the European champions the lead in the 36th minute, superstar captain Sam Kerr equalised with an extraordinary long-range solo goal in the 63rd to send the crowd of 75,784 into raptures.
But Kerr's heroics were in vain as Lauren Hemp scored eight minutes later to restore England's lead.
Kerr missed two late chances to equalise before Alessia Russo sealed victory with a third goal, and progression to Sunday's final against Spain, in the 86th minute.
"It was one of those nights - I've said it before - tournament football is won and lost inside the 18 (yard box) and England was clinical tonight," said Matildas boss Tony Gustavsson, whose side will face Sweden in Saturday's third-place play-off in Brisbane.
"We had a chance for 2-2 and a couple of minutes later it was 3-1. It was one of those games, unfortunately.
Gustavsson added of Kerr's stunning strike: "Knowing Sam, she probably thinks that goal wasn't worth anything.
"She wants to win and I'm happy for her that she got that. It proves who Sam Kerr is and what she can do.
"I also know that she's upset that she missed the two chances at the end of the game."
Australia must now pick themselves up for one final appearance on home soil.
Vice-captain Steph Catley said: "We do have another game.
"We were proud that we created history that we were able to get to a semi-final.
"But we ultimately believed that we could go all the way and do something really special."
Katrina Gorry worked tirelessly in midfield in her 100th cap but Australia were outclassed by England for much of the game and twice undone by poor work in defence, with centre-back Alanna Kennedy missing the match through illness.
Kerr, in her first start since her calf injury, was blanketed early but grew into the game, though Lucy Bronze and Jess Carter kept star winger Caitlin Foord quiet.
Emily van Egmond made way for Kerr in the starting line-up, while Kennedy was replaced by Clare Polkinghorne.
England opened the scoring with help from an Australian defensive lapse.
Hemp picked up a Rachel Daly throw-in and flicked it over Carpenter.
Russo pounced, weaved into space and quickly worked the ball back to an unmarked Toone, who buried a first-time shot into the top corner.
Australia appeared down and out with their superstar captain kept quiet, until the tireless Gorry slipped through Kerr and she took off.
Kerr went on a wonderful marauding run before cutting outside Chelsea teammate Millie Bright and launching an incredible long-range shot that beat star 'keeper Mary Earps.
But just eight minutes later Bright launched a long ball and Carpenter failed to deal with physical pressure from Hemp.
The attacker nipped the ball away from Carpenter before restoring England's lead.
"Obviously mistakes happen and that's football. It happens," Carpenter said.
Kerr headed over the bar in the 82nd minute while substitute Cortnee Vine forced Earps into a save a minute later.
Kerr blasted over the bar in the 85th and a minute later Hemp turned provider, slipped through Russo who fired low and into the bottom corner to round out the victory.
