Hunter, who became the most capped women's Test player, scored the first of seven tries in a match dominated by the English forward pack, who revelled in the wet, heavy conditions.
Flanker Marlie Packer bagged a hat-trick as all seven tries went to forwards - but none was more celebrated than when Hunter crossed in the seventh minute, off the back of a powerful scrum.
The veteran No. 8 was playing her 138th Test, surpassing the previous record held by former England prop and long-time team-mate Rochelle Clark.
"It's been amazing, I've tried not to think about it too much - you don't know what's going to happen so I just wanted to get out on the pitch," Hunter said.
"It's a really special day and now I can sit back and enjoy it."
Australia had no answer to the cohesion of England's pack and the tactical kicking of fly-half Zoe Harrison.
Those facets have been at the heart of a 29-match winning streak which has the Red Roses favoured to win a third world title.
However, Hunter says they can't get ahead of themselves.
"We're now in the business end of the tournament and we're going to have no easy rides along the way," she said.
"We'll look at this game and see where we need to work on and tidy up things."
England led 19-7 at halftime, boosted by a double to Packer while Australia's lone try went to flanker Emily Chancellor just before the interval, via the most exciting attacking movement of a dour spectacle.
Abbie Scott, Amy Cockayne, Alex Matthews and Packer crossed in the second half to set up a semi-final against Canada, who defeated the United States.
The Canadians scored two tries in each half, complemented by 12 points from the boot of captain Sophie de Goede.
De Goede said a team meeting on the eve of the match brought them together, as they reflected on the sacrifices made by many in what is effectively an amateur sport in Canada.
"We spoke a bit about what every person has gone through to get to this point," she said.
"For every player to come out here and perform the way we did, I'm just so proud of this group."
The US opened the scoring through a try to hooker Jojo Kitlinski but they failed to cross again as Canada's superior driving play set up tries to forwards McKinley Hunt and Karen Paquin before halftime when they led 12-8.
Backs Paige Farries and Alex Tessier made the result safe with tries, as the Canucks beat the US for a record seventh-straight time, a run which included last week's 29-14 win in group play.
The other semi-final next week will pit defending champions New Zealand against France after both were comfortable quarter-final winners on Saturday.
