The eighth-seeded Murray was denied his second career title. The first came earlier this year at the SAP Open in San Jose, Calif.
"I beat a lot of very good players and this gives me a lot of confidence," Clement said. "It's my fourth title, the second of the year, so I'm very happy with that. I played lots of tiebreaks this week and I won them all. I had to play my best tennis to win today and the first set was a very high standard."
"I definitely had my chances and should have won the first set," said Murray, who was playing for the first time under new coach Brad Gilbert.
The match changed when Murray was broken twice in the second set.