Thiem was untouchable behind his first serve and he saved all three break points he faced in the 10th game of the opening set to keep his serve intact and mount the pressure on the other side of the net.
Nadal hadn't lost a single set on clay since falling to Thiem a year ago in the Italian Open quarterfinals.
Describing Thiem as "one of the best players in the world", Nadal admitted that the Austrian player performed exceedingly well while he was never in a good position throughout the match. He had won the French Open and the hard-court US Open to take his Grand Slam haul to 16, and he came to the Spanish capital fresh off winning his 11th titles at both Monte Carlo and Barcelona.
Nadal will now officially lose his top rank to Federer when the updated ATP Rankings will release on Monday, but the 31-year-old can retain his top spot with a win at the Rome Masters, which begins on Sunday.
While Thiem admits the conditions in Madrid suit him perfectly - it is where he reached his first Masters 1000 final a year ago - he also believes he produced exceptional tennis to overcome the King of Clay.More news: Footage from scene of Offaly light aircraft crash
Fittingly, Thiem won the match with a blazing cross-court forehand victor, and Nadal was left to shrug his shoulders in helpless fashion.
On Wednesday, Nadal notched another bit of history on clay, winning his 50th consecutive set on the surface and breaking John McEnroe's record of 49 straight on the same surface set back in 1984.
He saved the first break point, but then tried to hit a risky forehand that sailed long, allowing Nadal to level the set at 3-3. The most recent meeting was in the 2017 Citi Open, a match Anderson won in three sets. "Small things happen that normally when you're in a good momentum, those things don't happen".
In the semi-finals Saturday, Thiem will face Kevin Anderson, the South African who was a finalist at the last U.S. Open. If he plays well, I just need to stop him.
"Of course I am disappointed", Nadal said. "To beat Rafa on clay you have to have a special day".
Dutchwoman Kiki Bertens continued her remarkable run at the Madrid Open by thrashing French seventh seed Caroline Garcia to reach the womens' final.