Dane Caroline Wozniacki, seeded fifth this year, was dumped out by American 24th seed Coco Vandeweghe, while Russia's Svetlana Kuznetsova returned to the quarterfinals after a 10-year hiatus by beating Polish ninth seed Agnieszka Radwanska.
It was a heartbreaking blow for Nadal who arrived at the tournament fresh from a record-setting 10th French Open title with genuine belief that he could capture a third Wimbledon title and a 16th career major.
The newly-crowned 10-time French Open champion and world No.2 hadn't dropped a set - let alone a match - in two months before falling 6-3 6-4 3-6 4-6 15-13 to Luxembourg's daring left-handed serve-volleyer.
The victor of that match will have a chance to take on defending Wimbledon champion Andy Murray in the semifinals, assuming this year's No. 1 seed beats American and No. 24 seed Sam Querrey in his own quarterfinal match. And he finished with nearly twice as many winners as errors-and a place in his first Wimbledon quarter-final. Health issues may have hampered him in the defeats to Darcis and Rosol but he pronounced himself fit this Wimbledon.
The Luxembourger reached his first quarter-final at the All-England Club, with a stunning near five-hour victory over the world No. 2 to set up a last-eight meeting with Marin Cilic.
"He played well and I didn't play well the first two sets", Nadal said. The No16 seed hit 95 winners against 52 unforced errors and won 59/83 points at the net. That cost me two sets against in the score.
So they headed to a fifth set, which was masterful, filled with brilliance from both.
Muller regained his serve and Nadal retained his for the two-plus hours of riveting tennis.
He dialled back in again in the sixth game and broke back but Murray at last found a flashing backhand victor to force another break and a chance to serve for the set. But the 15-time Slam champion came roaring back after looking dead in the water.
While Nadal failed to concede more than one point in any of his five services games during the set, a double-fault from Muller in the fifth gave Nadal the opening he needed to put together a three-game spree once again.
How it must have frustrated Muller, since he had rallied from 0-40.
Muller saved 14 break points in the match, including five in the fifth. Muller broke once in each set. He wish was granted. I make few mistakes, yeah, especially one that I went to the net.
Until Monday, Nadal had not lost a set in grand slam play since losing January's Melbourne Park final to Roger Federer. Murray, bothered by a hip injury in the buildup to Wimbledon, was in Nadal's half.