Australia were on the ropes at 14-3 in the seventh over when Smith forged an obdurate century partnership with Alex Carey, who batted for the major part of his 46 with a bandaged jaw after sustaining a nasty blow on his chin.
Australia captain Aaron Finch’s decision to bat appeared to backfire with Chris Woakes and Jofra Archer blowing away the Australian top order.
Archer figuratively drew first blood with his first delivery to dismiss Finch before leaving Carey with an actual bloodied chin.
By then, the setback had snowballed into a full-blown crisis for Australia.
Woakes removed David Warner, Australia’s leading scorer in the tournament, for nine and bowled Peter Handscomb who was making his World Cup debut as replacement for the injured Usman Khawaja.
Archer bowled with hostility, hitting a hopping Carey on the grill of his helmet and dislodging it from his head.
Carey braved the blow to join Smith in their dogged bid to arrest the free-fall and Australia reached the 100-mark in the 25th over before their middle order caved in.
Adil Rashid claimed 3-54, including the wickets of Carey and Marcus Stoinis, and Archer sent back Glenn Maxwell, who scored at a run-a-ball for his 22 before being deceived by a slower ball.
Smith was run out in the 48th over and Australia eventually folded with an over to go in their innings.
England have not reached the final since the 1992 World Cup and are chasing their maiden title.
The winners will take on 2015 finalists New Zealand in Sunday’s final at Lord’s.