Yorkshire's defending champions ousted in Qatar
Top seed Matthew, from Sheffield, went down 8-11 5-11 11-8 12-10 11-8 to allow Darwish the chance to meet fellow Egyptian Amr Shabana in Friday's final, after he defeated France's Gregory Gaultier.
The defeat was Matthew's second in less than two weeks from the position of a 2-0 lead - after crashing out of the Kuwait Open to England team-mate Daryl Selby.
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Hide Ad"Karim did well to come back from 2/0 down," said Matthew. "It's really a good effort, well done to him.
"You are never too old to learn. Now there's a few weeks of hard work for the Worlds - whatever the result here, that's always been my target."
"Nick has been winning pretty much everything last year, he was world number one still a few months back, so beating him tonight is very special to me," added Darwish. "When I can play like that, I'm alright."
Leeds's James Willstrop's hopes of success were ended at the quarter-final stage when he was defeated 2-11, 14-12, 11-4, 11-7 by second seed Shabana.
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Hide AdIn the women's draw there was also disappointment for Harrogate's Jenny Duncalf, also a defending champion, after she was beaten 9-11 11-5 12-10 11-5 by Australia's Rachael Grinham, who meets Nicol David in the final.