Murray, playing in his first tournament since losing his fourth Australian Open final, was unusually profligate, committing numerous unforced errors from his usually rock-solid groundstrokes.
The Scot slipped 5-1 behind in the first set before playing some of his best tennis to break back once, but eighth seed Simon held firm to take the opener in Rotterdam.
Simon continued to outmanoeuvre Murray in the second set and forged 4-0 ahead before the Briton again offered some stiff resistance, threatening to get back to 4-3.
There was no reprieve for Murray though and Simon completed victory on his third match point to set up a semi-final with defending champion Tomas Berdych who beat Gael Monfils.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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