Australia have not won at Edgbaston for 12 matches in all formats at Edgbaston since an Ashes Test success in 2001, with that run including a group defeat by England in the last Champions Trophy four years ago.
The victor of Sunday's clash will likely take on Bangladesh in their semi-final in Birmingham on Thursday, the first time the Tigers have reached the semis of a major tournament, while England will head to Cardiff to probably play the victor of Monday's match between Pakistan and Sri Lanka.
Eoin Morgan said the potential of Ben Stokes is "through the roof" after having the best view in the house as the all-rounder's stunning century helped England knock Australia out of the Champions Trophy.
Stokes than continued the chase with Jos Buttler (29 n o, 32b, 3×4, 1×6) before rain again interrupted play at 240/4 in 40.2 overs.
Rashid's four for 41 included a spell of three for four in 10 balls as he and Wood - with a career-best four for 33 - wrecked Australia's hopes of upping the ante in the last 10 overs after reaching a promising 220 for four.More news: Patty Jenkins Still Not Signed On For Wonder Woman Sequel
Warner's fall brought in his captain Smith, who along with Finch steadied the ship to take the visitors to the three-figure mark. Morgan deserved a hundred but was run out for 87 when Adam Zampa pulled off a direct hit from mid-on.
At 136-2, Moises Henriques joined Smith and the duo brought up the 150 in 25.3 overs.
Coming into the must-win match against England, my biggest concerns from an Australian point of view were that England had confidence and momentum, and because it had already qualified for the semi-finals, could play with freedom, which is a unsafe recipe.
Hosts England takes on Australia at Edgbaston in the final match which is Group A. Australia will be under pressure this time as anyhow this time Australia have to win the match.
Asked how they had revived England's innings, Morgan added: "They (Australia) bowled really well up front and got the ball moving". However, less than six overs into England's innings things didn't look quite so bright; their first three batsmen back in the shed with only 35 runs on the board, including another failure for the under-fire Jason Roy.
Smith (56) fell to Wood, while Jason Roy sensationally caught Glenn Maxwell (20).More news: U.S. urges Saudi allies to ease Qatar blockade
But his memorable boundary catch - staying just inside the foam marker initially, then throwing the ball up as he went out of bounds before returning to complete the play - was outstanding, and kickstarted a telling rush of wickets.
Eoin Morgan on the match-winning partnership with Ben Stokes and the chat they shared before heading to the crease after a short rain break: "We just talked about how we were going to go about it".
Stokes completed a 39-ball half century featuring eight fours when he hooked Starc for six, with Morgan following him to the landmark in 51 balls.
England's vibrant, attacking style, has been credited in the local media with following a blueprint set by New Zealand under Brendon McCullum.
With rain not showing any signs of rescinding sooner, the match officials declared England the victor of the contest by 40 runs as per the duckworth lewis method.
Maxwell's exit was the start of a collapse that saw Australia lose five wickets for 15 runs in 26 deliveries. But once Stokes creamed two back-to-back fours off Pat Cummins, Australia's goose was cooked.More news: UK's Labour leader Corbyn sees possible new election this year or next
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