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.
“At this tournament, it’s really nice that I know I can play my best tennis,” Halep said.
The second-ranked Wozniacki needed to win the title in Madrid to overcome Halep for the No. 1 spot.
“At this tournament it’s really nice that I know I can play my best tennis,” said Halep, who next plays Karolina Pliskova, the sister of her opponent on Wednesday, in the quarterfinals.
The Associated Press contributed to this report.