The Lionesses had stumbled at the same stage twice before but the European champions made no mistake this time to reach the final for the first time.
They took the lead nine minutes before the break with Manchester United's Ella Toone unleashing a rocket just inside the box with the outside of her boot.
A fit-again Sam Kerr, starting for the first time this tournament, hit back for the home side in the second half with a world-class goal that set the game on fire, picking up the ball and letting fly from 30 yards after a weaving run.
It sparked ecstatic scenes from the 75,784-strong partisan crowd.
But they were silenced eight minutes later when Hemp muscled her way into the box and stabbed into the corner before Russo put the icing on the cake with four minutes left.
England now face a blockbuster final on Sunday at the same Stadium Australia against a dangerous Spanish side that beat Sweden 2-1 in the last four, with a new name to be engraved on the trophy.
England had been in this position before, in 2015 and 2019, losing 2-1 on both occasions, with a third-place finish their best World Cup before now.
But coach Sarina Wiegman led them to the European title last year on home soil and captain Millie Bright said before the match they were now better-placed to handle big-pressure games.
They demonstrated their resilience at a pumping and partisan Stadium Australia, successfully blanking out the noise to silence an expectant home nation.
Victory was all the sweeter against an opponent who had beaten them 2-0 in an April friendly — the only side to do so in 38 games since Wiegman took over.
Despite losing Australia have enjoyed their best World Cup ever, with a third-placed playoff against Sweden on Saturday still to play.
With Kerr fit again, Australian coach Tony Gustavsson moved Emily van Egmond to the bench in one of two changes with defender Clare Polkinghorne in for an ill Alanna Kennedy.
England stuck to the same XI that beat Colombia 2-1 with striker Lauren James serving the second of a two-match ban.
Both sides were nervy in the opening exchanges but Australia settled and a lofted ball through the middle from Katrina Gorry left Kerr with just goalkeeper Mary Earps to beat.
But the Manchester United stopper repelled the shot, with the offside flag later raised.
At the other end, fellow keeper MacKenzie Arnold rescued Australia minutes later, deflecting Georgia Stanway's strike with her legs as the game opened up.
Kerr was in the thick of the early action and England ruthlessly looked to close her down with some heavy challenges, one of them earning Alex Greenwood a yellow card.
But as England grew in confidence they began controlling the midfield battle.
The breakthrough came in the 36th minute with Toone, in the side for James, arrowing her shot into the top right corner after Hemp pulled the ball back from the touch line.
With 45 minutes to save their tournament, Australia frantically pressed forward as the second half got under way and it paid dividends when Kerr's wonder strike propelled them back into contention.
But England were unmoved and when Ellie Carpenter misjudged a long ball into the box, Hemp hustled her way through to score, before Russo finished calmly with her right foot to seal the win.