The 26-year-old Hsieh Su-Wei, on the other hand, deserved all the joys from her first victory against a world No.1 as she fought back from a 2-5 deficit in the decider.
The 32-year-old will make her first appearance in the Wimbledon last 16 when she faces Slovakian world number 33 Dominika Cibulkova on Monday.
"It's unbelievable. I was 2-5 down in the final set but the crowd pushed me to fight".
In a sport often dominated by relentless baseline bashers Hsieh brought so much more to the party.
Hsieh saved the match point with a backhand victor before holding for 5-5 and broke Halep in the next game.
Jiri Vesely, Czech Republic, def. Fabio Fognini (19), Italy, 7-6 (4), 3-6, 6-3, 6-2.
Her unique style of play drove Halep to distraction as Hsieh unfurled a series of drop-shots, delicate slices and seemingly innocuous ground-strokes.
Jelena Ostapenko, the 2017 French Open champion, also went safely through after she swept aside Vitalia Diatchenko in straight sets.
Williams, 36, who gave birth to her daughter in September, has dropped to 183rd in the world after playing only three tournaments in the last 12 months but is seeded 25th at Wimbledon having received a favorable draw by organizers.
The biggest threat to Nadal reaching the last four could well be fifth seed Juan Martin del Potro, who is through to the fourth round for the first time since 2013 after a 6-4 7-6 (7/4) 6-3 victory over Frenchman Benoit Paire.
"It was a positive match against a player with a lot of energy", said Nadal, the 2008 and 2010 champion. It's really tough to stay low, to play every ball, to expect actually nothing because you never know where the ball is bouncing and where is coming.
Simona Halep's defeat means there is only one top ten women's seed remaining.
Van Uytvanck will meet Russian 14th seed Daria Kasatkina, who beat Australia's Ashleigh Barty 7-5, 6-3. Also physically I feel exhausted. She wouldn't win another game.
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