"I was serving well again today and returning well. That's what I was working on in the off-season so it already pays off now," Thiem said.
Croatian Coric was expected to overcome Rublev after beating Pablo Carreno Busta in the opening round but the 20-year-old Russian won 6-3 7-5 to set up a semi-final against Guido Pella.
Both Pella and his quarter-final opponent Mirza Basic were surprise contenders in the last eight after knocking out top seeded players and the Argentine world number 64 cruised to a 6-2 6-3 victory over the Bosnian.
World number five Thiem will face Gael Monfils in the last four after the Frenchman beat German Peter Gojowczyk 6-3 7-6(6).
(Reporting by Aditi Prakash in Bengaluru, editing by Ed Osmond)
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