Nadal routed Maximilian Marterer in straight sets to advance to the quarterfinals in pursuit of his 11th French Open title and his second in as many years.
Sharapova and Williams were due to clash in the fourth round on Monday but the American pulled out at the last minute of their eagerly-awaited grudge match with injury. A win at Roland Garros - her third - would equal Williams' slam record here and would be the icing on the cake of her comeback.
A pectoral muscle injury had slammed the brakes on the ruthless Williams's serving arm so she decided not to take up the opportunity to extend her 14-year, 18-match win streak over the Russian.
Her voice trembled a bit as she explained that she will get an MRI exam and consult with doctors before figuring out what will happen next for her.
In Paris, Williams was playing her first Grand Slam since winning the 2017 Australian Open when she was two months pregnant and first since she gave birth to daughter Olympia in September.More news: Trump says Russian Federation should be let back into the G-7
Sharapova also wished her speedy Recovery.
However, the big story from Paris on Monday focused on a match that didn't even go ahead after three-time Roland Garros champion Williams withdrew from her last-16 clash with long-time rival Sharapova. She picked the muscle pain during her third round match with Germany's Julia Georges.
"It was really painful", Williams said, "and I didn't know what it was". And that's why it's been hard to play for her.
"At the end, she was just pushing the ball...."
This is the first time since 2005 that two Argentines have made it to the Roland Garros quarter-finals in the men's singles draw, with Juan Martin del Potro also joining Schwartzman in the last-eight. The second set was tied 3-3 at the time, with Woz hoping to turn things around after losing the first set in a tight 5-7, but the 21-year-old Russian came out strong and won three games in a row to clinch the win, and is now into the quarters. Muguruza, who is 3-1 against the No. 1-seeded Halep in her career, has never squared off with her in a Grand Slam. Did she want to play mixed too? "I was trying what I could, but it just wasn't enough".More news: Macron: G7 leaders must be civil as they pressure Trump
The first round of the grass court Grand Slam is set for July 2 in London.
Kerber is set to take on Simona Halep of Romania, who thrashed Elise Mertens of Belgium 6-2, 6-1.
Runner-up to Jelena Ostapenko a year ago and to Sharapova in 2014, Halep needed less than an hour to see off a rival boasting three trophies in 2018 plus a 12-win streak this season on clay. The No. 3-seeded Muguruza missed the quarterfinals at the US Open and Australian Open after her win at Wimbledon previous year, so she's hoping to make an even deeper run to replicate that success.More news: CBS Sports: Kaepernick's Lawyers Expected to Subpoena Trump in NFL Collusion Case