After captain Aaron Finch hit an even 100 to lead Australia to 7-285, Behrendorff and Starc took nine of England’s 10 wickets to roll them for 221 in reply.
The result guaranteed Australia a semi-finals spot and left England’s hopes in doubt, sitting fourth with two big games to play after entering the tournament as favourites.
But crucially for Australia it gave them a potential eye to the rest of their tournament, as they have swapped between quicks with questions asked about the depth behind Starc and Pat Cummins.
Behrendorff took 5-44 after being handed the new ball with Starc, swinging it considerably as the pair had England at 3-26 early.
“That’s where I guess one of my primary strengths lies, bowling up front, swinging with the new ball,” Behrendorff said.
“It was great to be given that opportunity to be able select, as well, with the wicket early doors.”
Behrendorff’s first wicket was a beauty, swinging back through the gate to bowl James Vince for a duck on the second ball of England’s innings.
Starc then got the key scalp of Joe Root when he trapped him plum in front for 8, before he had Eoin Morgan caught pulling at fine leg in his next over for 4.
Behrendorff later returned to have Jonny Bairstow (27) caught on the legside boundary, before mopping up Moeen Ali, Chris Woakes and Jofra Archer.
“We don’t often see (two left-armers), but I don’t see why we can’t,” Behrendorff said.
“Sometimes you play three right-armers, so why can’t we play two lefties?
“Mitch and I do do different roles throughout the team.”
Ben Stokes had meanwhile offered the only real resistance for England with 89.
But their hopes were all but ended when Starc (4-43) swung the ball back to knock over the left-hander with one of his renowned yorkers.
He now has 19 wickets for the tournament, taking his career World Cup tally to 41 at an average of 13.92 and strike-rate of 18.8.
“I’ve bowled a fair bit with Mitch Johnson in the past and it showed again today there’s no reason why you can’t play two left-armers,” Starc said.
“Especially when conditions suit and when the match-ups suit as well.”
Finch had earlier brought up his second century of the World Cup and his seventh against England with an even 100.
Australia’s captain got through a difficult early period where both he and David Warner (53) battled with the moving new ball, before accelerating into the innings.
He hit 11 boundaries and two big sixes over mid-wicket and mid-on off Moeen, before he was caught the ball after bringing up his century.
After the game, under-the-pump England captain Eoin Morgan denied his side’s World Cup hopes are in jeopardy after its third loss of the tournament, after Sri Lanka and Pakistan.
“But I certainly don’t think it’s knocked anybody in the changing room. Normally when we lose games of cricket, like I mentioned yesterday, we go back to what we do well. We’ll still strive to do that for Sunday’s game,” he said.
“The chances are in our hands.
“Everything is within our control. We just need to produce a performance worthy of winning either one or the next two games.”
Morgan bristled at a question suggesting England have a mental block about facing Australia in World Cups.
He also crankily dismissed claims from Behrendorff that his bowlers bowled too short early in the Australia innings, with Finch and Warner taking advantage by putting on 123 for the first wicket.
It was 27 years ago that Australia last tasted defeat to England in a World Cup, in Sydney in 1992.
Tuesday’s loss was all the more jarring for Morgan’s side, who had won nine of the previous 10 meetings between the sides.
“Of course he did,” Morgan said when told of Behrendorff’s claim.
“Early on, I don’t think we did bowl short.
“I’ve just been shown a highlight reel of short deliveries in which poor shots were played.
“They were supposed to be short. They were aimed at guy’s shoulder or armpit. I thought we didn’t have a little bit of green early.
“We made Australia play and miss a lot. But that’s his opinion and he’s entitled to it.”
England face India at Edgbaston on Sunday.
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