Published: 2017-07-11 02:14:40 BdST
The 31-year-old Nadal fought back from two sets down and saved four match points in a 135-minute minute fifth set in which he successfully served to stay alive nine times.
At the 10th time of asking, however, and with thousands of transfixed fans watching the drama unfold on the screen on the hill and on the edge of their seats on Court One, Nadal buckled under the relentless pressure exerted by an inspired Muller.
A miss-hit forehand gave Muller two more match points and this time he finished the job as a weary Nadal went long.
Sixteenth seed Muller, who served 30 aces and hit 95 winners, will play Marin Cilic in the quarter-finals.