The 16-time Grand Slam champion, coming off titles in Monte Carlo and Barcelona, beat Monfils, 6-3, 6-1. He has won 37 of his past 38 matches on clay, including 20 in a row.
Nadal improved to 17-1 overall on the season with his win over the 41st-ranked Monfils.
“I’m happy to start with a victory,” said Nadal, whose last loss on the dirt came against Dominic Thiem in Rome last year. “It was a very solid match in all aspects.”
Nadal is two sets away from breaking John McEnroe’s 1984 record of 49 straight sets won on a single surface. He will next face Diego Schwartzman, who defeated Feliciano Lopez 7-5, 2-6, 6-2. The 36-year-old Lopez will be the tournament director in Madrid beginning next year.
Seventh-seeded John Isner beat fellow American Ryan Harrison 7-6 (1), 7-6 (7), while eighth-ranked Kevin Anderson defeated qualifier Mikhail Kukushkin 5-7, 7-6 (3), 6-2 to set up a third-round match against Philipp Kohlschreiber, who beat Roberto Bautista Agut 6-3, 4-6, 7-5.
“I just felt like I did the right things,” Sharapova said. “Despite a slow start, I was still very positive.”
The second-ranked Wozniacki needed to win the title in Madrid to overcome Simona Halep for the No. 1 spot.
Halep beat Kristyna Pliskova 6-1, 6-4 to stay on track for a third straight title in Madrid. She will face her opponent’s sister, sixth-seeded Karolina Pliskova, who defeated Sloane Stephens 6-2, 6-3.
“At this tournament it’s really nice that I know I can play my best tennis,” Halep said.