Nadal beat Argentina's Schwartzman 6-3 6-4 on the clay to take his winning set streak to 50 and eclipse McEnroe's total which the American achieved on carpet in 1984.
Having received a bye in the opening round of the tournament, the Spaniard tennis maestro had yesterday kick-started his campaign in Madrid Arena with a comfortable 6-3, 6-1 win over French player Gael Monfils in a one-sided second-round clash that lasted one hour and 13 minutes.
World number one Rafael Nadal made it to the quarterfinals of the Madrid Open with a victory that broke John McEnroe's 34-year-old record for successive set wins on a single surface.
"When my career is over, these are things that are going to be there for always". I beat an opponent who is hard. "Well, it's done. It's over".
"Let's not talk about that any more and let's focus on what we have ahead".
The win earns Nadal a date with the talented fifth seed Dominic Thiem, who came back from a set down to defeat Borna Coric 2-6, 7-6 (5), 6-4.
"On this surface, (Thiem) is one of the most risky players you can face", Nadal said.
Sharapova also lost in three sets to Kiki Bertens of the Netherlands while Halep, the champion in 2016 and 2017, was blown away by Karolina Pliskova.
The thrilling match went deep into the third and was still anyone's at 6-6 in the tiebreaker. "That's all", Nadal told a news conference.
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Nadal was broken just once in his 6-3, 6-4 win, while winning 68% of his first service points. Schwartzman broke back, but two straight double-faults gave Nadal a third break en route to the win.
The fourth seed Juan Martin del Porto fell in the last 16 after losing a tense three-set battle 3-6, 6-4, 7-6 (6) to the unseeded Croatian, Dusan Lajovic.
Lajovic will now face South Africa's Kevin Anderson, who overcame Philipp Kohlschreiber. Edmund, an unseeded Brit, defeated former No. 1 Novak Djokovic in straight sets on Wednesday.
The 31-year-old said there is still a way to go as she gears up for Roland Garros.
"I don't know if these kind of records are very important", he said, before adding, "I don't say I don't care because it's better to have these kind of things than don't have it". "I feel unbelievable since in the last six matches I lost to her".
Nadal took the opening set easily over Schwartzman having broken the Argentine's serve in the sixth game.
It means Pliskova, the sixth seed, is the highest-ranked player left in the women's draw after Caroline Wozniacki, Garbine Muguruza, Elina Svitolina and Jelena Ostapenko all lost earlier in the week. He will play German Alexander Zverev, who beat Argentine Leonardo Mayer 6-4 6-2.
Bertens, meanwhile, will now face France's Caroline Garcia, who eased past Carla Suarez Navarro 6-2, 6-3.