England secured a first World Cup win over Australia in 24 years and boosted their hopes of reaching the last four with a three-run victory in Bristol.
After Tammy Beaumont's 49, Katherine Brunt (45 not out) and Jenny Gunn (39) combined to push England to 259-8.
Ellyse Perry struck 70 but England held their nerve to the last ball and restricted Australia to 256-8.
Victory takes England above Australia and India to the top of the table on net run-rate with two games to play.
The first of those for the co-hosts comes on Wednesday against fourth-placed New Zealand, who are a point behind Heather Knight's side.
With a final game against a West Indies side who beat Sri Lanka to claim their first win of the competition on Sunday, England will be confident of securing a semi-final spot via a top-four finish.
It was a defeat by Australia in the last four of the 2016 World Twenty20 that prompted coach Mark Robinson to re-model the England side into its current guise.
In Delhi, they capitulated under pressure, leading Robinson to question their ability to execute even the most basic skills.
While there were occasional signs of fragility in Bristol - most notably through a couple of dropped catches that fortunately did not prove costly - this was a far more resolute and professional display.
Four times Australia produced partnerships of more than 40 but each time England stuck to the task and broke them.
Chasing what, in truth, was an under-par 260 target on a relatively flat track, Australia's openers Beth Mooney (31) and Nicole Bolton (26) put on 56 together before Alex Hartley dismissed the former and Gunn the latter in the space of three overs.
Meg Lanning and Perry came into this game with a partnership average of 104.07 and looked to be guiding the holders into a winning position by adding 57 together but again England struck back as Hartley bowled the former for 40.
This left Perry, who continued the push but lost two key partners in Elyse Villani (14) and Alex Blackwell (21) before she too fell, caught by Natalie Sciver off the bowling of the impressive Brunt.
It was a crucial wicket but not the end of Australia's challenge as first Alyssa Healy and Ashleigh Gardner and then Jess Jonassen kept up the chase.
Needing 10 from the final two balls, Australia were kept alive by a misfield from Sciver to concede four, but Jonassen was unable to find the maximum she needed from Gunn's last ball.
England's World Cup campaign has so far been characterised by a positive intent with the bat, which has seen them twice post totals in excess of 370, during which four players have scored centuries.
Having won the toss and opted to bat, England once again demonstrated that bold, attacking play in Bristol, but unfortunately for the hosts it was coupled with an inability to execute by their in-form top order.
England were indebted to Gunn and Brunt, who struck 85 between them, including five fours and three sixes, to push them beyond 250 and to an ultimately match-winning total.
Coming together at 174-6, the pair initially steadied the ship
Some credit must go to Australia, who deployed their plans well to dismiss Lauren Winfield (1) and Heather Knight (2) cheaply, as well as the initially ominous-looking Sarah Taylor (35) and Sciver (29) before they could get going fully.
Leg-spinner Kristen Beams proved particularly effective, bowling tournament top-scorer Taylor, via an inside edge, with her very first ball before prompting skipper Knight into a misjudged lofted drive straight to Lanning at mid-off.
This left opener Beaumont, who continued conservatively with the more aggressive Dani Wyatt to add 54 in just over 10 overs before both fell in relatively quick succession.
Again, poor shots cost were largely the cause as Beaumont fell caught and bowled to Gardner for 49, while Wyatt was bowled sweeping by Jonassen for 27.
'We were clinical' - What they said...
England captain Heather Knight: "I always knew we batted deep. Our line-up is firing at the moment. It was a frustrating batting display; we got the momentum then would lose wickets. Brunt and Gunn batted well for us today.
"It was probably about a par score. We knew how deep Australia bat. It was our best bowling display; we were clinical. It was a brilliant game but a hard one to captain.
"We have two big games coming up. When you're in the habit of winning you want it to carry on."
England bowler Katherine Brunt, player of the match: "It's always a show with England and Australia and I'm glad we can put on a performance today. I had fun. Us girls down the lower order have had a lot of practice and I back us to do that.
"To finish with 259 gave us confidence to go out and defend it. As a bowler, I don't like playing on these flat pitches; the batters have it too good. But credit goes to all the bowlers.
"It's always nice to get one up on the Aussies but this is just one game and there are a fair few to come."
Analysis: 'England kept fighting'
Former England batter Ebony Rainford-Brent on BBC Test Match Special
In some ways, it was a scrappy England win. I don't think they were at their best with the bat at times, or with the ball, but what they did was keep fighting.
The turning point was Alex Hartley getting in the game. When she took the wicket of Lanning, it changed the nature of it. The bowlers kept coming in. Jenny Gunn kept things tight and used her experience.
These two have not met for two years and they were always going to test each other but what a game. Well done England.
