
The Austrian will face Rafael Nadal, who is looking for his 10th title in Barcelona, or Argentina's Horacio Zeballos on Sunday.
Murray squeezed past Albert Ramos-Vinolas in a three-hour encounter on Friday and looked flat-footed as Thiem roared through the opening set with three breaks of serve in just over half an hour.
The Scot had to stave off another break point in a marathon opening game to the second set.
But he held on and then jumped at his chance to break for 5-3 before serving out to take the match to a decider.
Murray, though, still looks a pale shadow of the player that rose to number one on a spectacular run at the end of last year as he struggles for form and fitness after an elbow injury.
Thiem had to battle back from a break down in the third, but constantly put pressure on the Murray serve and broke another three times in the deciding set to seal his place in the final.
"It's the first win over a World No. 1, so it's really something special," said Thiem who added it would "be a great honour to play Nadal".
"But it's also the first win over a Top 10 guy this season. There are many positive things to take from today's match.
"For me personally, it's the best victory this year so far. I went down in the third set when he broke me in the first game. But the way I came back mentally was a huge step forward today."
Murray squeezed past Albert Ramos-Vinolas in a three-hour encounter on Friday and looked flat-footed as Thiem roared through the opening set with three breaks of serve in just over half an hour.
The Scot edge the second set with the only break, but still looks well short of the player that rose to number one on a spectacular run at the end of last year as he struggles for form and fitness after an elbow injury.
Thiem had to battle back from a break down in the third, but constantly put pressure on the Murray serve and broke another three times in the deciding set to seal his place in the final.
However, having accepted a late wildcard to play in Barcelona, Murray believes the match practice will do him good with Masters series events in Madrid and Rome to come ahead of next month's French Open.
"I got three matches in three days against all different players," said Murray.
"To play two hours today after three yesterday, will be good for me."