With his 21st consecutive straight-set victory on clay dating back to last year's French Open, Nadal also set an Open Era record for most sets won in a row (50) on a single surface, reports Efe.
The previous holder of that mark, American great John McEnroe, won 49 straight sets on the carpet in 1984.
The 31-year-old Nadal, a five-time winner of this French Open tune-up event, used his powerful groundstrokes to break Schwartzman's defense and run his career record against the Argentine to 5-0.
The Spaniard lost his serve only once during the one-hour, 44-minute third-round match, with the Argentine using a strong down-the-line backhand to earn that break in the eighth game of the second set.
But Schwartzman proceeded to let the match slip away by dropping his serve in the ensuing game.
Asked afterward about his latest record-breaking achievement on his favourite surface, the "King of Clay" said he did not give much importance to it.
"I really don't think much about that. All these things, probably after I finish my career will be the time to think about it," Nadal was quoted as saying on the ATP World Tour's Web site. "I won a difficult match against a very difficult player that played well."
Next up for Nadal in Friday's quarter-finals will be Austrian world No. 7 Dominic Thiem, who rallied to edge Croatia's Borna Coric 2-6, 7-6 (7-5), 6-4 in the third round.
Thiem is the last player to defeat the 10-time Roland Garros champion on clay, achieving that feat nearly one year ago at the 2017 Italian Open.
The Spaniard said the fast conditions in Madrid made the 24-year-old Austrian, who also has had his best results on clay, a particularly challenging opponent.
"Very tough match. Especially here on this surface and even more in altitude. His bounces and topspin are very high and difficult to control," Nadal said.
"I need to be ready for tomorrow. It will be a very tough match to play but it's a good opportunity to play against one of the best players of the world," he added.