Nadal's 50 straight set wins on clay sees him surpass McEnroe's 1984 record.
The Masters 1000 Series continues throughout this week with our coverage of the ATP Madrid Open quarter-finals on Sky Sports Arena starting from midday.
"When my career is over, these are things that are going to be there forever", Nadal said. But being honest, I don't know if these kind of records are very important. "Well, it's done. It's over".
While new records are always just around the corner, the world No. 1 is focused on titles.
McEnroe also won the Madrid Open Indoor title that year and Nadal may be about to follow suit in the Spanish capital, with Austrian Dominic Thiem up next in the quarter-finals on Friday.
"On this surface, (Thiem) is one of the most unsafe players you can face", Nadal said.
The women's defending champions and top seed, Simona Halep brushed past qualifier Krystina Pliskova 6-1, 6-4 in just 75 minutes, but the second seed Caroline Wozniacki surprisingly lost 6-2, 6-2 to Kiki Bertens, who is now ranked 21st in the world.
The top-ranked Nadal, who improved to 18-1 overall on the season, has won 38 of his last 39 matches on his favored clay.
Schwartzman made an impressive start to the match, surviving a couple of break points on his first service game before setting up an opportunity of his own.
Nadal then struck a forehand victor on the run to break Schwartzman again in the second set.
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Schwartzman was not finished yet and broke for the first time to level at 4-4 after giving Nadal the runaround with some powerful groundstrokes off both wings.
But while the world number one cruised to a 6-3, 6-4 victory over Diego Schwartzman, Juan Martin del Potro, Maria Sharapova and Simona Halep all crashed out.
Zverev will now come up against Isner, a 6-7 (9-11), 7-6 (7-3), 7-6 (7-4) victor against Pablo Cuevas on a bad day for the South Americans, in a rematch of the Miami Open final won by the American.
Denis Shapovalov defeated fellow Canadian Milos Raonic 6-4, 6-4 to advance along with Kevin Anderson and John Isner.
The 31-year-old said there is still a way to go as she gears up for Roland Garros.
Pliskova gave the Romanian no chance, breaking her serve four times and hitting 20 winners.
"Even in the warm-up I felt so good today", Pliskova said. "I feel wonderful since in the last six matches I lost to her".
Nadal must have forgotten what it feels like to go to the distance, though, and a double fault from Schwartzman put the Mallorca native back in front and he was jumping for joy after serving out the match to make history.
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.
Second seed Zverev showed no signs of tiredness as he cruised past Mayer 6-4 6-2 in only 70 minutes.