There were some fascinating exchanges, but after cruising through the first set, Thiem was more clinical.
Although he threw in a double fault while serving for the match at 5-3 up in the second set, the Austrian dominated the tie break and sealed his place in the semi-finals.
The top seed at the event is now one win away from securing his place at the season-ending ATP World Tour Finals in London next month.
Murray – who was facing a top-10 player for the first time since his comeback from hip surgery – had 29 winners come off his racket.
But Thiem was far superior in other departments, with 48 of his 70 points won at the net.
He made 16 unforced errors, but got 66 per cent of his first serves in and produced seven aces.
Speaking after his defeat, Murray said: “I think there were some really good points in the match, like at the beginning of the match some really good points [and] also at the end.
“I was a little bit unsure kind of how to go about the match at the beginning… I was feeling a little bit tired this morning.
"We talked about maybe, ‘If you are feeling that way, try to finish off some of the points’… I wasn't that happy with the way I went about the match after the first game. I went a bit off track there at first, in terms of how I was playing. The week overall was good.”
Thiem – who has landed three titles on the ATP Tour this season – will face Karen Khachanov in the last four.