The third-seeded former champion will face eighth seed Tomas Berdych after the Czech dispatched Juan Monaco 6-3, 6-4 to extend his perfect record against the Argentine to 7-0.
Murray, who won the title at Crandon Park in 2009 and 2013, was initially stunned by the clean and powerful one-handed backhand of the 21-year-old Thiem. "I expected a tough match, Thiem's beaten some very good players this week," said Murray, who needed one hour and 44 minutes to seal the win. "He's a very big hitter of the ball, a very strong guy and he moves extremely well.
"When you let him dictate the points, he hits the ball as hard off each side as anyone. He made me do a lot of running."
Meanwhile, Berdych took 92 minutes to get past Monaco, producing a pair of love service games and a break in the final three games to capture the tight second set and seal the win.
"It wasn’t easy but I'm very happy to go through,” said the winner. “My focus was to stay as close as possible with him and try to create opportunities.
Serena to face Halep after 700th match win
Serena Williams marked another milestone on Wednesday, punching her semi-final ticket at the Miami Masters with her 700th career match win, a 7-6 (7/4), 1-6, 6-3 triumph over Sabine Lisicki.
Serena will face a familiar foe for a place in the final, taking on popular Romanian Simona Halep, a 6-1, 7-5 winner over Sloane Stephens.
"I didn't know I had 700, now I just want to keep going, doing the best that I can," said the 33-year-old American, who was feted with a cake from tournament organisers after the victory.
Third-seeded Halep dominated Stephens, racing to a 6-1, 3-0 lead before the American dug in. Stephens won five of the next six games to take a 5-4 lead in the second but couldn't force a third set.
"I'm really happy I played like this, it was an amazing match for me," said Halep. “I'm glad that I finished in two sets and stayed focused until the end."
Halep has some history with Serena. The Romanian is the last woman to beat the US superstar on the WTA tour, humbling the world number one 6-0, 6-2 in the round robin phase of the WTA Finals in Singapore in October.
Serena rebounded quickly — beating Halep 6-3, 6-0 in the final days later.
"I just have to play aggressively against Serena like I did today at the beginning of the match," said Halep. "I think this is the most important thing to do to have any chance against her."
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