The world No. 59 has had a solid clay-court season so far, winning his first career singles title in Marrakech last month.
Coric played well above himself but this was a poor performance from Murray, arguably his most disappointing since losing in the fourth round of the Australian Open.
"I couldn't imagine this when I woke up this morning, I always believed but I wasn't sure how I was going to play, but in the end I played as I had dreamed", Coric told Television Espanola.
Coric broke the fragile Murray serve three times in the first set under the roof at the Manolo Santana centre court due to rain in the Spanish capital.
Murray also lost at the last 16 stage in the Monte Carlo Masters, his first tournament after recovering from an elbow injury, and was beaten by Dominic Thiem in the semi-finals of the Barcelona Open.
Novak Djokovic progressed into the quarter-finals with a more convincing display that on Wednesday, when he defeated Feliciano Lopez 6-4, 7-5 in straight sets.
His frustration boiled over in the eighth game of the second set as he lashed a backhand well wide to go 0-40 down on his own serve.
"It's not always the worst thing losing a match, but it's sometimes the manner of how you lose the match is what can be concerning or disappointing".
The Belgian will now play Spain's Rafael Nadal after he saw off Australia's Nick Kyrgios 6-3, 6-1.
Uruguay's Pablo Cuevas recovered from losing the second set 6-0 to beat Benoit Paire and will meet Germany's AlexanderZverev, a 6-4 6-4 victor over Tomas Berdych.
Djokovic faces a much tougher test on Friday against world number eight Kei Nishikori, who earlier swept aside David Ferrer 6-4, 6-3.
David Goffin awaits the victor of that clash after the Belgian beat world number six Milos Raonic 64, 62. I was in trouble and I managed to get my way out of it with some great gets.
At 3-4 there seemed no undue cause for concern from the Scot's point of view but then he threw in a slew of groundstroke errors to be broken, and there was an absence of any fightback as Coric served it out.
Meanwhile, among the women, Eugenie Bouchard ousted Angelique Kerber to reach the quarter-finals.
France's Kristina Mladenovic also made it through to the final four.
Syrian Kurds welcome U.S. arms, Turkey objects
The US responded to this strikes by carrying out joint patrols with the YPG, at the strike area on the Syria-Turkey border. Canikli said Turkey would take the diplomatic initiative to convince Washington "to do what friendship requires".