The Spaniard, a 15-time Grand Slam winner, came from two sets down to level the match, but was ultimately beaten 3-6, 4-6, 6-3, 6-4, 13-15 by the 16^th seed after 4 hours and 48 minutes - the longest match of this year's tournament so far. 

Defeat ends Nadal's hopes of winning back-to-back French Open and Wimbledon titles for a joint record third time.

"I'm tired," Muller, who took a fifth match point to seal his victory, told BBC Sport. 

"It was a long match - I was two sets up, I played well then Rafa stepped it up and then it was a big battle.

"I had match points and didn’t make them - it was getting tough and I was watching the sky thinking that would be over soon. 

"Then in the last two match points I thought just give it a shot and go 100 per cent. 

"It’s a great feeling."

Muller's reward is a quarter-final encounter with Croatia’s Marin Čilić, who eased to a 6-2, 6-2, 6-2 win over Spain’s Roberto Bautista Agut.

Defending champion Sir Andy Murray is also through to the last eight after defeating France’s Benoit Paire 7-6, 6-4, 6-4.

Next up for the Briton is a meeting with American Sam Querrey, a 5-7, 7-6, 6-3, 6-7, 6-3 victor at the expense of South Africa’s Kevin Anderson.

Seven-time champion Roger Federer booked a quarter-final spot thanks to a comfortable 6-4, 6-2, 6-4 victory over Bulgaria's Grigor Dimitrov.

The Swiss will go onto face Milos Raonic in the quarter-finals after the Canadian downed Germany’s Alexander Zverev 4-6, 7-5, 4-6, 7-5, 6-1.

The other quarter-final pits Czech Republic’s Tomas Berdych against either Serbia's Novak Djokovic or France's Adrian Mannarino.

Berdych came through a five-set match against Austria’s Dominic Thiem, triumphing 6-3, 6-7, 6-3, 3-6, 6-3.

Djokovic and Mannarino are due to play their fourth-round match tomorrow. 

In the women’s singles event, Spain's Garbine Muguruza beat top seed Angelique Kerber of Germany 4-6, 6-4, 6-4 to reach the quarter-finals.

Awaiting the 14th seed is Russia’s Svetlana Kuznetsova, who defeated Poland's Agnieszka Radwańska 6-2, 6-4.

Defeat for Kerber means she will lose her world number one ranking as she had needed to reach final to have a chance of retaining top spot.

Romania's Simona Halep will replace Kerber as world number one if she reaches the semi-finals.

Halep overcame Belarus’ Victoria Azarenka 7-6, 6-2 today.

Standing between her and a place in the last four is Johanna Konta, who becomes the first British woman since Jo Durie in 1984 to reach the quarter-finals of Wimbledon with a 7-6, 4-6, 6-4 win over France’s Caroline Garcia.

Five-time champion Venus Williams moved into the quarter-finals with a routine 6-3, 6-2 win over Croatia's Ana Konjuh.

The 37-year-old American, seeded 10th, will take on French Open champion Jelena Ostapenko of Latvia in the last eight.

Ostapenko beat fourth seed Elina Svitolina of Ukraine 6-3, 7-6.

Slovakia's Magdaléna Rybáriková, ranked 87th in the world, qualified for her first Grand Slam quarter-final with a 6-4, 2-6, 6-3 victory over Croatia’s Petra Martic.

Rybáriková next goes up against American Coco Vandeweghe, who beat former world number one Caroline Wozniacki of Denmark 7-6, 6-4.