When Muller edged Nadal 6-3 6-4 3-6 6-4 15-13 on so-called "Manic Monday" -- each player remaining in both singles draws was scheduled to take to the court -- it ended the Spaniard's bid for a third French Open-Wimbledon double.
The absorbing fifth set alone lasted 135 minutes, with Nadal finally succumbing on a fifth match point when he sent a forehand long. He had saved two match points at 4-5 in the fifth with two fine serves of his own and then two more at 9-10.
But 16th-seed Muller also showed great courage, fending off four break points a game earlier.
How Nadal will rue those missed opportunities, especially since on at least two he probably should have won the point.
"Rafa stepped it up in the third and the fourth set," Muller told reporters. "Then I just told myself, 'Look, I mean, I'm doing the best I can. I'm playing well. Just hang in there and you're going to get your chances.'
"Got a few of them. Didn't take the first ones. But still kept believing. Yeah, somehow in the end I made it."
Overall, Nadal went a mere 2-for-16 on break points, while his fellow left-hander was a considerably better 3-for-8. Muller struck 30 aces to Nadal's 23.
"That's not the result that I was expecting," Nadal told reporters.
Having previously downed Nadal at Wimbledon in 2005, the veteran from Luxembourg became just the sixth man to get the better of the 31-year-old at least twice at grand slams: He joined the illustrious quintet of Roger Federer, Novak Djokovic, Andy Murray, Lleyton Hewitt and David Ferrer.
Despite Nadal not contesting a grass-court warmup this year, he was considered one of the favorites at the All England Club given that record-extending 10th success at the French Open last month -- and his form overall in 2017.
Set streak ends
He compiled a whopping 28-set winning streak at grand slams prior to running into the 34-year-old in the fourth round on Court 1, lifting his ranking to second in the world behind Murray following an injury-ravaged 2016 and taking him closer to the No. 1 ranking he last held in June 2014.
Nadal has been on the wrong end of upsets before at SW19, exiting to Dustin Brown in the second round in 2015, Steve Darcis in the first round in 2013 and Lukas Rosol in the second round in 2012.
Indeed not since advancing to the final in 2011 has Nadal -- the Wimbledon champion in 2008 and 2010 -- landed in the quarterfinals here. Health issues may have hampered him in the defeats to Darcis and Rosol but he pronounced himself fit this Wimbledon.
"It's true that I played some good matches, but at the same time it's true that I didn't want to lose this match," said Nadal. "So it's tough to analyze that in a positive way right now.
"Yeah, I won matches. I played better than other years. At the same time I was ready for important things, so I lost an opportunity."
Muller, however, is a cut above Brown, Rosol and Darcis. He is having the best year of his career despite his advanced tennis years, capturing a first title in Sydney in January and claiming a grass-court title in the Netherlands two weeks ago.
No one has won more matches on grass in 2017 than Muller, a former junior No. 1.
Now he has earned a spot in a second grand slam quarterfinal, nine years removed from his first.
He said that sustaining an elbow injury in 2013 was probably a blessing in disguise. When he returned he was a different player.
"Because I had problems with my elbow, I wasn't able to touch a racket," said Muller, who will challenge another proficient grass-court player, Marin Cilic, on Wednesday. "I was able to work out physically, I got myself into the best shape I ever was.
"Since 2014 when I came back, I'm able to play full seasons without any breaks during the season. I have a lot of confidence in my body now, which I didn't do before. All this is changing a lot for me. For sure that has been the key for me in the last few years, to be that successful."
Perhaps Nadal bumping his head while warming up in the tunnel heading into Court 1 -- he and Muller shared a laugh -- was a sign of things to come for the Mallorcan.
When play began, the first two sets followed a similar pattern.
Nadal earned the first break points, at 2-3 in the first and 4-3 in the second, but was unable to capitalize.
With chances always bound to be limited on the fierce Muller serve -- he entered Wimbledon fifth in aces in 2017 -- not breaking serve appeared to unnerve Nadal. He was broken in the ensuing games and Muller didn't blink on serve.
Backed by the majority of the crowd on a sun-kissed afternoon, though, the 15-time grand slam winner got down to business in working himself back into the encounter.
He broke for the first time at 3-1 in the third, unleashing a vicious inside-out forehand. For the rest of the third set and much of the fourth, Nadal managed to consistently apply pressure on the Muller serve.
Undaunted by squandering two break points at 1-1 in the fourth, Nadal broke on his fourth break point in the fifth game when Muller sent a backhand into the net.
How it must have frustrated Muller, since he had rallied from 0-40.
Muller took a toilet break ahead of the fifth and the pause appeared to have helped, since the venom on his serve returned. Serving first in the set was a bonus for Muller, since he was able to apply more pressure on Nadal with each hold.
Nadal celebrated wildly as he continued to save the match points -- to the crowd's delight -- and there was yet more drama before the final game when he asked for a panel that was reflecting sun into his eyes to be covered. His wish was granted.
But the sun went out on his dream of a third Wimbledon title courtesy of one of Luxembourg's few tennis exports.
Federer, Murray win in straight sets
Nadal's departure truly opens the door for defending champion Murray, who along with Federer advanced in straight sets. Murray, bothered by a hip injury in the buildup to Wimbledon, was in Nadal's half.
Murray defeated Benoit Paire and Federer -- Nadal's conqueror in Melbourne -- swept past Grigor Dimitrov.
But the fourth member of the Big Four, Djokovic, didn't get his match started with Adrian Mannarino because of the length of Nadal's tussle. Organizers opted not to switch him to Centre Court, even though the last match on Centre ended early.
Djokovic will surely have his say on the matter Tuesday when he speaks to reporters.
In the women's draw, French Open champion Jelena Ostapenko continued to win -- beating Elina Svitolina -- but top seed Angelique Kerber was beaten by Garbine Muguruza.
In Tuesday's women's quarterfinals, Venus Williams -- the lone former Wimbledon winner still in the women's draw -- plays Ostapenko; home hope Johanna Konta meets French Open finalist Simona Halep; 2015 finalist Muguruza faces two-time grand slam winner Svetlana Kuznetsova; and CoCo Vandeweghe plays maiden grand slam quarterfinalist Magdalena Rybarikova.