The Mallorcan surpassed John McEnroe’s previous record of 49 consecutive sets on carpet which had stood since 1984 by seeing off 13th seed Schwartzman and claiming a 21st consecutive win on clay.
Nadal will face Austrian Dominic Thiem in the last eight on Friday in pursuit of a sixth Madrid Open title after beginning the claycourt season by winning an 11th Monte Carlo Masters and lifting the Barcelona Open trophy for the 11th time.
Nadal said he was unaware of the record.
“These moments I don’t go out there and think about these kinds of things. I just think about my opponent, what I have to do to keep on going. That’s all,” Nadal told a news conference.
“When my career is over, these are things that are going to be there for always. They are big records. It’s difficult to be able to win 50 sets in a row. But I’ve done it. Let’s not talk about that anymore and let’s continue on what we have ahead.”
In the quarter-finals, Dusan Lajovic surprised Juan Martin del Potro 3-6 6-4 7-6(6) and will meet South Africa’s Kevin Anderson who overcame German Philipp Kohlschreiber 6-3 7-6(7).
Britain’s Kyle Edmund followed up his surprise win over Novak Djokovic by defeating world number 10 David Goffin to reach the last eight of an ATP Masters 1000 event for the first time in his career.
The 23-year-old broke his Belgian opponent’s serve twice in the opening set and once in the second, to seal a 6-3 6-3 victory in an hour and 12 minutes.
“I managed my game very well,” the Briton said. “My game is better the better I manage it and pick the moments not to be aggressive.
Edmund will next face Canadian teenager Denis Shapovalov, who achieved a 6-4 6-4 win over compatriot Milos Raonic.
“It was definitely one of my best days on clay,” said 19-year-old Shapovalov, who is ranked 43rd in the world, 19 places below Raonic. “To be on the court against such a legend for me, and for my country, it was an honour.
“What (Raonic) does for our country, for tennis, for these past couple years, it’s incredible. To beat him, it was a huge confidence booster for me.”
American John Isner also advanced to the quarter-finals after overcoming Uruguayan Pablo Cuevas in a tight match 7-6(9) 7-6(3) 7-6(4). He will play German Alexander Zverev, who beat Argentine Leonardo Mayer 6-4 6-2.
