The 19-year-old Sindhu, who clinched the bronze at the 2013 World Championship in China, produced another gritty performance to see off All-England champion Shixian Wang of China 19-21 21-19 21-15 at Ballerup Super Arena here.
Earlier this month, Sindhu had won a bronze at the Commonwealth Games in Glasgow, Scotland.
Earlier, Olympic bronze-medallist Saina, seeded seventh, struggled against World No.1 Li Xuerui and the Chinese took just 45 minutes to send the Indian packing with an identical 21-15 21-15 scoreline.
In the quarterfinal contest that lasted for one hour and 25 minutes, Sindhu and Wang were locked in a battle of attrition and rode on each other's mistakes to gather points.
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Sindhu dominated the net early on and used her height and reach well to lead 11-5 initially. However, Wang soon caught up at 15-15 before getting past the Indian to pocket the first game.
A couple of unforced errors helped Sindhu to narrow the gap but the Indian faltered at the forecourt to help Wang keep the lead. The Indian kept fighting and used her smashes and better judgment of the shuttle to draw parity at 16-16.
Wang, however, faltered at the nets to allow Sindhu a 19-16 lead and then hit another miscued shot to give the Indian four-game points.
The decider started with a long rally which Sindhu grabbed after Wang hit wide. The Chinese kept hitting wide and long and found the net allowing the Indian to lead 5-2. But Wang once again caught up at 5-5.