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.
The hard-hitting batsman scored 68 runs off 64 balls and formed a vital 96 runs partnership with Smith which gave his team a foundation to their innings.
Wood and Rashid took four wickets each, ripping through the middle of the Australian batting order.
With England already through to the semifinals, pressure was on Australia to perform after washouts against New Zealand and Bangladesh hurt their chances of making the last four.
Their win ensures Bangladesh will finish second in Group A ahead of Australia and therefore enter the semi-finals of the competition.
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Standard & Poor's said Wednesday it has lowered its long-term rating on Qatar one notch to AA-, its fourth-highest level. Most of Qatar's gas exports go to Asia via sea - 72 percent according to the U.S.
Their partnership contained 106 runs in boundaries, with Morgan clubbing eight fours and five sixes before getting run out by Adam Zampa after a mix-up going for a single.
Durham quick Wood returned ODI best figures of four for 33 in his maximum 10 overs, while Rashid's haul of four for 41 was the Yorkshireman's best against a Test nation at this level.
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 risky recipe.
As Australia head home from their damp-squib campaign, and England set their sights on Wednesday's semi-final in Cardiff, Morgan and his opposite number Steve Smith both acclaimed Stokes.
But from 136-1, Australia failed to surge to the 300-plus score in their sights as Finch skied Wood to Morgan in the covers and Moises Henriques (17) picked out mid-on off Rashid after a promising start.
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May's party is short of the 326 it needed for an outright majority and fairly down from the 330 seats it had before the election. Mrs May's decision to seek a deal with the DUP has prompted concerns from some Tories. "This is still on", Corbyn says.
However, Stokes (102*) combined with Morgan (87) to pull England back from the abyss and put them on course for a win. The wicket-taking balls which were in abundance in their first three overs were then few and far in between.
Finch nonetheless had his highest one-day global score in more than a year, from only 64 balls with eight fours.
Smith completed a 68-ball fifty, including five fours, with a sweetly-timed off-drive against Plunkett.
England's win put Bangladesh through as the other semi-finalists from Group A with Mashrafe Mortaza's men in action back here on Thursday. The players jogged off and didn't return, sealing a victory for England by 40 runs using the Duckworth-Lewis-Stern scoring method.
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Treasury's Office of Foreign Assets Control, or OFAC, for a license to see the deal through, it said in an emailed statement. However, the deal could be scuppered if US President Donald Trump goes ahead with threats to reimpose sanctions on Iran.