The winner of this match faces New Zealand in the final at Lord's on Sunday.
Smith acknowledged his fourth half-century of the tournament, this one off 72 balls, reinforcing his stellar record in knock-out matches. Promoted to No.3, he appeared to enjoy the added time he had to build an innings.
As wickets tumbled, Smith ensured he would be the batting plank his side needed. He shared in an eighth-wicket stand of 51 off 59 balls with Mitchell Starc and was only dismissed by a brilliant direct hit by wicketkeepeer Jos Buttler when attempting a single in the 48th over.
Carey, praised by Steve Waugh for his calmness and even touted by the Test legend as a specialist batsman in the Ashes, had been promoted from No.7 to No.5 after a strong campaign. He had made 46 off 70 balls before he took on the longest boundary of the ground - deep mid wicket - but his clip off Rashid lacked power and he was caught in the deep by substitute fieldsman James Vince.
He later required stitches on the cut but was given the all clear to take the wicketkeeping gloves.
This brought Marcus Stoinis to the crease, and Rashid had his second wicket two balls later when the allrounder was fooled by a wrong-un, leaving the Australians at 5-118 after 28 overs.
The day began well for Australia when David Warner (9 off 10 balls) stroked the first ball of the match, from Woakes, for four through cover but disaster came on the corresponding delivery of the next over.
Finch - who has seven centuries against England - became the first captain ever in a World Cup knock-out clash to fall first ball when trapped lbw to Archer. That was the blueprint for Finch - full and fast into his pads. And it worked a treat.
That brought Smith to the crease, and he received the now cliched boos upon his arrival. Warner looked to turn the pressure back on England, delivering a lofted drive to the boundary off Woakes. But the quick had the ultimate response, producing a back-of-the-length delivery which squared the former vice-captain up and induced a tickled edge to second slip.
There were more boos when Warner trudged from the field but the Australians were more concerned about the dispiriting scoreline of 2-10 off 2.4 overs.
Peter Handscomb (4 off 12) was the only change from the side beaten by South Africa, and that was forced, for the injured Usman Khawaja could not be considered. This wasn't going to be easy for the Victorian, thrust into the biggest one-day international of his career without having had played a game this tournament.
It was no surprise, then, that there was more drama when Handscomb survived an lbw shout off his first ball that prompted England to call for a video replay.
The Australians needed to show fight, for this was a brilliant opening spell from Woakes and Archer.
Unlike at Lord's when Archer pitched too short, he asked questions of the batsmen here with an excellent line and pace. So, did, Woakes, and he found another answer on the first ball of the seventh over when Handscomb pushed forward and a hint of movement exploited a gap between bat and pad. This early carnage left Australia wobbling at 3-14 - their worst start ever against England in a one-day international.
Carey was then hurt by a brutal bouncer which drew blood and lifted the helmet off the batsman. In a rare sight, he instinctively caught the helmet, a fortunate occurrence for had he not, it may have hit the stumps. Team doctor Richard Saw was required, and plastered the right side of Carey's chin.
He remained at the crease, and responded soon after with a delightful cover drive off Woakes for four.
Carey required more treatment after the 13th over, this time having strapping under the chin and around his head.
Glenn Maxwell (22 off 23 balls) won a selection reprieve but again failed with the bat, this time when he was fooled by an Archer knuckle ball and spliced to short cover.
Jon Pierik is cricket writer for The Age. He also covers AFL and has won awards for his cricket and basketball writing.