Captain Sarah Hunter scored the Red Roses’ opener on the day the 37-year-old became the most-capped England and women’s international with 138.
All seven of England’s tries came from forwards in the wet weather and flanker Marlie Packer completed a hat-trick.
Emily Chancellor scored Australia’s only try in the first half.
Abbie Ward, Amy Cokayne and Alex Matthews all crossed too as England extended their record winning run to 29 Tests in a row.
The Red Roses last won the World Cup in 2014 and will face Canada in Saturday’s semi-final, with a potential final against New Zealand or France to come.
England power on through the rain
New Zealand had claimed a concerningly dominant victory against Wales in their quarter-final on Saturday, but as the rain poured onto the Waitakere pitch it was clear England would not be able to follow suit.
Instead of the exciting running rugby displayed by Black Ferns stars Portia Woodman and Ruby Tui, England had to settle for victory by force.
On a day that felt more like the English autumn than the Auckland spring, puddles splashed up with every footstep and England turned to their powerful pack as captain Hunter went over first at the back of a scrum.
While the Red Roses are professional, Australia are amateur and committed errors they could not afford against such well-drilled opponents.
England went down to 14 players as lock Zoe Aldcroft was shown yellow for a dangerous clearout at the ruck, but it did not slow their charge.
Fly-half Zoe Harrison continued to show smart kicking, scrum-half Leanne Infante looked lively and centre Tatyana Heard was an attacking threat as she played for a previously unlikely semi-final starting spot.
Australia captain Shannon Parry was sent to the sin-bin for repeated infringements near the tryline and after a couple of frustrated attempts England eventually made it over again.
Packer’s first score came in a trademark driving maul, then she cut through a gap for a second try after slick passing from England’s forwards.
Heard was left with too much to do defensively after her earlier impressive attacking work and missed a tackle on Australia prop Liz Patu to ensure England’s opponents could end the half on a high as flanker Emily Chancellor scored.
Packer leads forwards’ charge
England have never failed to reach a World Cup semi-final and, after the rain stopped at half-time, they continued to exert their dominance over a side that has never beaten them.
Ward went over from short range minutes after the break, then Cokayne fought her way over after a line-out.
With victory surely secured at 29-5, England head coach Simon Middleton made changes after 50 minutes.
The Red Roses front row of Cokayne, Vickii Cornborough and Sarah Bern – celebrating her 50th cap – came off along with Hunter, who was given a loud cheer from the numerous travelling support.
Matthews finished another forwards try before Packer completed her hat-trick with one last line-out drive.
It was not always a stylish victory in the conditions, but got England to where they needed to be nevertheless.
What they said
England captain Sarah Hunter: “We are used to playing in the rain, but that was something else. It was all about the victory, I thought we played very well. Sure there were mistakes but we asserted our game on Australia.
“We’ve had four tough games, now it’s about recovery and working out where things didn’t go so well today. We have to have the right game plan for the semi-final.”
And on winning her 138th cap: “It’s been amazing. I’ve tried not to think about it too much as you never know what is going to happen. But it has been a really special day and now I can sit back and enjoy it.
“I just want to say thank you to my amazing team-mates and everyone who has supported my career from the age of nine to now.”
England head coach Simon Middleton: “I said to them at the end, we could not have imagined how difficult those conditions were. We managed it brilliantly, played in the right areas and took our chances brilliantly.
“What about Sarah Hunter, on her record performance? That’s so Sarah, every time we needed a carry she was there.
“It was impossible to handle the ball, it was about getting in the right field positions and letting the forwards go from there.”
Line-ups
England: Rowland; Thompson, Scarratt, Heard, Dow; Harrison, Infante; Cornborough, Cokayne, Bern, Aldcroft, Ward, Matthews, M Packer, Hunter (capt).
Replacements: Davies, Botterman, Muir, Galligan, Cleall, L Packer, Aitchison, Kildunne.
Australia: Piliae-Rasabale; Terita, Friedrichs, Williams, Cramer; McKenzie, Morgan; Patu, Talakai, O’Gorman, Leonard, Kemp, Chancellor, Parry (capt), Hamilton.
Replacements: Naden, Robinson, Karpani, Naiqama, Duck, Batibasaga, Smith, Murphy.
