In a meeting between the players with the most match wins this year, Nadal saved all five break points he faced against the 10th-ranked Belgian, and converted his chances in the second set to win his 13th straight match. Murray lost 6-3 6-3 in less than an hour and a half, exiting at the third round stage for the first time in three years.
The Scot delivered too many errors against a highly concentrated opponent in going down to his sixth defeat of the season.
Twelve months ago, Murray was moving through the gears at the Mutua Madrid Open before hitting top form and going on to take the world rankings by storm.
Coric came into the game in fine form, having secured his first ATP Tour title in Morocco last month.
Despite the pressure of serving for the match, Coric remained cool to seal victory in just under 90 minutes on court when Murray fired wide to set up a quarter-final clash with Thiem.
The player, who is now ranked 49th in the world, outplayed Murray, who has been in poor form of late and only recently lost in the semi-finals in the Godo Tournament in Barcelona. Murray was sensational on the red-stuff in 2016, as he was on every surface, but it is easy to forget that before last season he had traditionally struggled on clay.
Andy Murray was left frustrated by his inability to change the tide in his surprise straight-sets defeat to Borna Coric at the Madrid Open.
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Those who don't want it removed are arguing that it belongs to a park board, and therefore the city has no authority to remove it. Critics of the monuments say they foster racism by celebrating leaders of the pro-slavery South during the US Civil War.
Rafael Nadal set up a semifinal with Novak Djokovic after withstanding a tough challenge from David Goffin 7-6 (3), 6-2 at the Madrid Open on Friday. "That's concerning. So I need to think about exactly why that is, what I can do about it".
But Murray eventually made his move and let out a cry of joy with a brilliant cross-court half-volley to break Copil's resistance and take the first set 6-4. "I started the match okay, but when I started to go behind, I didn't find any way to improve my game or to make it more hard for him", Murray told a news conference. As you saw today, I could have lost the match, so it doesn't matter who is winning, who is losing.
"The level was definitely very high today I thought from both of us". Whereas today I didn't really do any of that stuff. The second-seeded Djokovic will play veteran Spaniard Feliciano Lopez, who got past Gilles Simon of France 6-3, 3-6, 7-6 (3). "You need to kind of hold your nerve, hold your concentration, and use all the necessary energy at the right moments".
Nadal was coming off titles in Monte Carlo and Barcelona and had made it to three finals earlier in the year.
In the Women's Madrid Open defending champion Simona Halep cruised back into the final for the third time in four years with a 6-2, 6-3 over Latvia's Anastasija Sevastova.
"Hopefully I can do that with my team, and play better in Rome and Roland Garros".