Slovene Bedene saved 12 out of 15 break points to push the Austrian but the world number five survived the test to be the only seed left in the draw, apart from Frenchman Richard Gasquet, who won the event in 2013.
Yet world number 31 Gasquet, the fifth seed, was surprisingly beaten 6-3 6-4 in the late match by Greece’s rising talent Stefanos Tsitsipas, with the 19-year-old from Athens progressing to face Thiem in the next round.
Seventh-seeded Fernando Verdasco was defeated 6-4 3-6 6-4 by Russian youngster Andrey Rublev, while eighth seed Feliciano López suffered a shock 6-4 7-6(2) loss to Bosnia’s Mirza Bašić, who is ranked 138th in the world.
The Spanish duo joined high-ranking players Pablo Carreño Busta, Tomas Berdych, Albert Ramos Viñolas, and Filip Krajinović in exiting the tournament in the early stages.
In the quarter-finals, Rublev, 20, will face Croatia’s Borna Ćorić, who ousted Carreño Busta in the first round, while Bašić will take on Guido Pella after the Argentine overcame Stefano Travaglia 7-6(4) 6-3.
French wildcard Gaël Monfils beat Jan-Lennard Struff 6-3 1-6 6-3 to set up the other last-eight clash with German Peter Gojowczyk.