Having slipped to 166-7, a 51-run eighth wicket partnership between Smith and Starc took the visitors past 200 but England took two wickets in two balls - a brilliant direct hit from wicketkeeper Jos Buttler at the non-striker's end running out Smith for a tournament-best 85 before Mitchell Starc (29) nicked Woakes' next delivery behind.
The Eoin Morgan-led side produced a scintillating bowling performance and followed it with as sound batting show, leaving Australia in shambles. "They absorbed a bit of pressure, saw that swing was going to be a little bit of a threat and the way they waited until the bowlers came into their areas to hurt them was very smart", said Joe Root, who saw England through to victory with a brisk unbeaten 49 from 46 balls.
By contrast, Australian captain Aaron Finch did his best to put a courageous face on Australia's first-ever semi-final defeat after seven previous triumphs. And it was the very first ten overs of the game in which the semi-final was lost, Australia left dazed, confused and nearly down at 27 for 3.
Edgbaston exploded with noise as Finch, David Warner and Peter Handscomb were removed, cheers that were matched in volume by the boos for Warner and Smith.
As it became clearer that England were strolling, the party moved through the gears.
Roy smashed his fourth consecutive fifty in the tournament, clobbering Smith for three sixes in a row.
This was a complete display by England, who were magnificent with the ball, sharp in the field and dominant with the bat.
"Chris Woakes and Jofra Archer bowled a hell of a spell". Jofra Archer got the big scalp of and Chris Woakes sent back unsafe David Warner and young Peter Handscomb to reduce Australia to 14/3. He dismissed Jonny Bairstow, taking his wickets tally for this World Cup to 27.
"I think that as a management, senior players, I'm sure over the next next couple of months or so we will sit down and start talking about that and start planning how we think that we can best plan and prepare and improve over the next four years to get us to go, well two steps further".
Given their team for this tournament only really came together at the last minute, it is to Australia's credit that they made the semi-finals with such ease.
Indian fans hurt by World Cup exit but proud of team
Pre-tournament favourites India had topped the group table to book the semi-final clash with fourth-placed underdogs New Zealand. Never before did the first three batsmen of a team got out for one run each in a match.