Nadal extended his winning streak to 50 consecutive sets on clay, eclipsing the mark McEnroe established on carpet in 1984.
"When my career is over, these are things that are going to be there for always. It's difficult to be able to win 50 sets in a row," Nadal said. "Well, it's done. It's over. Let's not talk about that any more and let's continue on what we have ahead, which is what I am concerned about."
The world No. 1's focus is trained on his next match against Dominic Thiem, a rematch of last year's final. Thiem, who outlasted Borna Coric 2-6, 7-6 (5), 6-4, is the last player to beat Nadal on clay, at Rome last year.
"On this surface, [Thiem] is one of the most dangerous players you can face," Nadal said. "Tomorrow is a key match in the tournament."
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.
Nadal went up a break at 4-2 in the first set after back-to-back errors by Schwartzman, including a missed smash.
Nadal then struck a forehand winner on the run to break Schwartzman again in the second set. Schwartzman broke back, but two straight double-faults gave Nadal a third break en route to the win.
The 16-time Grand Slam champion is seeking his sixth title in Madrid after taking his trophy hauls at Monte Carlo and Barcelona to 11 apiece.
In other men's matches, second-seeded Alexander Zverev brushed aside Leonardo Mayer 6-4, 6-2 and will meet John Isner, who edged Pablo Cuevas in a hard-fought match that needed tiebreakers to decide all three sets.
Isner prevailed 6-7 (9), 7-6 (3), 7-6 (4) in 2 hours, 21 minutes.