Victory on Sunday would see Nadal become the first player to win the same grand slam 10 times in the modern era. But Thiem, who said he played one of his best matches that day, couldn't replicate his top level as Nadal rolled throughout their seventh FedEx ATP Head2Head meeting.
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A couple of dazzling ground-strokes, including a forehand victor, gave Wawrinka a second break and, with it the set.
Wawrinka, who hoisted the trophy in 2015, blasted 87 winners on Friday to out hit Murray from the baseline.
At 3-0 in the third to Wawrinka, things looked bleak for Murray, but he moved a little closer to the baseline while continuing to pull off some incredible recovery shots.
Moreover, Wawrinka has won three Grand Slam titles in recent years, the first of which came in 2014 when he beat Nadal in the Australian Open final.
Murray is still not quite at the same level as he was a year ago, when he played probably his best clay-court match to defeat Wawrinka and then went on to dominate the second half of the season. "You need to, as I say, keep pushing yourself".
Andy Murray knows he will have to be at his best again if he is to defeat Stan Wawrinka and reach the French Open final for the second consecutive year.
He coughed up a break advantage and the lead in the third set which allowed Murray to take the two-sets-to-one advantage, forcing Wawrinka to dig deep over the next two sets.
How Wawrinka holds up physically after such a long duel with Murray will no doubt be something to ponder, but he is extremely strong and a year ago at the US Open defeated Novak Djokovic in the finale after tough matches along the way. But Wawrinka's now won four of their five encounters on clay courts. "So that's the thing that I am more proud", said Nadal.
The record books might not interest the 31-year-old Mallorcan, but he will have to be dragged away screaming and kicking before giving up the chance to move into double figures and land La Decima against Stan Wawrinka on Sunday.
Crucially for Wawrinka, he didn't waver mentally, after blowing a 5-3 lead in the first set - and holding a set point on his own serve in the first-set tiebreak - and 4-2 in the third.
"Hopefully it gives me a good base to go into the grass court season".
"I don't know how close I am to that", Murray said. I'm just going to try my best.
Simona Halep advanced to the semifinals of the French Open after saving a match point, beating Elina Svitolina 3-6, 7-6 (6), 6-0. However, that just prolonged the inevitable as Wawrinka broke again to take the set 6-1.
Wawrinka booked his place in his fourth Slam final with another stylish backhand down the line victor.
The second-seeded Djokovic had two set points in the opener but couldn't convert either.